WEEK 11 8/10

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• How to Virtual Unary Pml Sludenl Concern MARK !VAN NAROO ■
Oa shbo1ml SHS-GR11-15 PREC-111 Week 11 Key Concepb of Circular Functions Trigonomelrit Iden lilies, ln ve~e Tri9onome tric: Functions and Pol ar Coordinate System - Part 001 ShortOuiZ9

QUIZ NAVIGATION C-Jul>Ol\ 1 Determine two coterminal angles (one positive and one negative) for each angle Give your answer in degrees using the foDovting forma t ex. 34. -25

Finish attempt

Timelefl0:15:48
L
Answe r : 405, -315

Determine !he quadrant in which each angle kes The answer should be in the folowing formal ex_ Quadrant I

:.:~
M1rtedout,;,I
a.1 30 "

--
,00 Answer: OuadrantH
"Flag

C:lub0n 3 Determine the quadrant in winch each angle &es The answer should be m the folowmg format ex. Quadrant I

::.:::., d-336'

"""'M" Answer: Quadrant!

"'
l"fllg
"'""Dan
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• How to Virtual Unary Pml Sludenl Coni::em MARK !VAN NARDO ■
SHS-GR11-15 PREC-111 Week 11 Key Concept$ of Circular Functions Trlgonomebic Identities, In ve rse Trigonometric Functions and Polar Coordinate System P;>irt 001 ShortOuiZ9

Determine th e quadrnnl m which each ;mgle ~es The answer should be in the fol owi n9 formal ell'.. Ouadr;,nt I
c. -132 " 50

Answer: Ouadrantm

a.a..oon5 Determine the qu;,dr;,111 m which e;,ch ;,119le Ues The ;,nswershould be in the fol owmg format ell'.. Qu;,dr;,nt I
b.2ss·
"""'
M ......

~ruc! Olll of
Answer: OuadrantlV
"'
I'"'•
.,H_

Findlhe;,n9leinro1di<1ns

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O.nhbo;,rd SHS-GR11-1S PREC-111 Week 11 Key Concepts of Circu!;,r Functions. Trigonomebic Identities, In verse Trigonometric Functions ;,nd Polar Coordinate System P;,rt 001 Short0uiz9

Answe r : 5

..-
~
Cl<titxx1 7
,. Findlhe ;,n11le inro1di;,ns.

G
~ ruc!Olll of

"'
.,H _
f' Flag

Answer: 1

-
o..= 8 Determ111e two coterminal angles (one p ositive ;>ind one negative) for each an11 le Give your answer 10 degrees usIn11 the fo~owin11 format: ell'._34, -25
Nol~

M~ outof
, oo
I'"'•
"'"-
Answer. 324, -396

Finishaltempl

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WEEK 12
Dn hc-oard • SHS -O'l:11 -1S PRE C-111 Wee~ 12: Key Coi,cepu ofC>!'Cular FwnellOl"<S Tngooorrun;; k!ennt'.Ei, lnvem1 Tng<l<"olN!toc: F1.rt'II01'5 ai,dPola r Coordlf\ate System - FanOJ2 S~onC.i.: 10

Smtedon TYe5di.y, 170etober2017, 1 ~2FM

QUIZ NAVIGATION

Comple1edon TY1!roay, 170ctober201i'. \ · ~ F M

r1meQken 7rrun•2Dsecs
Grade 10.00outol 10 00 (100~~)

=:va,.. ate fd panibll!) the soc tngonomelllC t.mc':Klns or tte 1nl ~umber If not possiba, answer w,:11 ·undemed

'= .:;

d c~(-i) = -1

., 5C:C(-i)" i,nd,...-..,.,;

: va!i,ate!hesJ11 e. cos.neandwgen:oft!:eiealr.umberW!rte · ll!'defined"tlll'ino1pos.ible

I •ln(-1f) = ·,2,2

2 ro{-Zf) = 212

l ~(-If) = 1

Cva.1.. at;: ihe ~onome::ric function t. Q Jl5 J)='.riod as a.r a d.

c11mi:1: 1: sin 5r
r.t,: rkt CC.O.t\1:1'
, c,
Answe,r: 0

ai:~sr;!::in 4 se th-= value of:he trigonometric fu:11:tion to evaluat': tte dic3'ted fu ctions.
C.:,.mi;l: t~
sin t = H3
,.., ,: rkt CC.OJIC'
•OJ
i. c.sc(-t,
V R.:J:
Answer: -3

S.ta:e tfle q.u 3dra ,1 in vmtcil e lies:

Su: i:f >O a d '.3n 8< 0

Answer: Qua<lrant U

WEEK 13
Dashboard SHS-GR11 -1S PREC-111
Week 13: ~ey Concepts of Circular Functions,
Tri,gonome iric Identities; Inverse Trigonometric Functions
and Polar Coordinate System. - Part 003
Learning Activity 11

Find the period and amplitude .

-

Select one:
a.. Period: n, Amplitude: 3

b. Period: 2n,. Amplitude: a

Dashboard SHS-GR11 -1S PREC-111
Week 13: ~ey Concepts of Circular Functions,
Tri,gonome iric Identities; Inverse Trigonometric Functions
and Polar Coordinate System. - Part 003
Short Quiz 11

Find the period and amplitude.

Select one:
a.. Period: 4n, Amplitude: 5/2

b. Period: 2n,. Amplitude: a

Dashboard SHS-GR11 -1S PREC-111
Week 13: ~ey Concepts of Circular Functions,
Tri,gonome iric Identities; Inverse Trigonometric Functions
and Polar Coordinate System. - Part 003
Learning Activity 11

b.

A= -4

d= 4
Dashboard SHS-GR11 -1S PREC-11 1
Week 13: ~ey Concepts of Circular Functions,
Tri,gonome iric Identities; Inverse Trigonometric Functions
and Polar Coordinate System. - Part 003
Short Quiz 11

Mark 1.00 out of 1.00

1

Flag question

Find the p,eriod and amplitude.

y= -2 sin x

Select one:
a. Period: 3n, Amplitude: 1/2
b. Period. 1,.Amplitude: 1/ 4
,c. Period: n/.5, .Amplitude: 3
d. Period: 2n, Amplitude: 3
Dashboard SHS-GR11 -1S PREC-111
Week 13: ~ey Concepts of Circular Functions,
Tri,gonome iric Identities; Inverse Trigonometric Functions
and Polar Coordinate System. - Part 003
Short Quiz 11

Mark 1.00 out of 1.00

Flag question

Find the period and amplitude.

y- 2
= -cos-.
2 3

Select one:
a.. Period: 2n, AmpUtude: 3
b. Period: n/5, Amplitude: 3
c. Period: 3~ Amplitude: 1/2

d. Period. 1, Amplitude. l/4

Dashboard SHS-GR11 -1S PREC-111
Week 13: ~ey Concepts of Circular Functions,
Tri,gonome iric Identities; Inverse Trigonometric Functions
and Polar Coordinate System. - Part 003
Learning Activity 11

Find a and d for the funcUon f(x) -

a cos x + d such that the graph of f
:m atches the figure.

a.

.A= 2

d= 1
Dashboard SHS-GR11 -1S PREC-111
Week 13: ~ey Concepts of Circular Functions,
Tri,gonome 1ric Identities, Inverse Trigonometric Functions
and Polar Coordinate System. - Part 003
Short Quiz 11

Mark 1;.00 out of 1.00

Flag ,question

Find the period and ampJitude-

Y = 3sin 1.0x

Select one::
a. P.eriod: 1, Am:plitude:. 1/ 4

b. Period: 3n, .Amplitude: 1/2

,c. Period: 2tt Amplitude..3
d. Period: n/5, Amplitude. 8

WEEK 14
Dashboard SHS-GR11 -1S PREC-111
Week 14: Long Test Long Quiz 2

Find a form ula fo r the sum of the

fi rst n terms of t he sequenoe.

l 1 1
' .-
12 ,,-
2 J•-0.

Select one:
n
a. sn -- -
2(n --)

. n
b. Sn= - -
(n-1)

, n
c. Sn= - -
2(11 )

n
d. Sn = - -
n+l
Dashboard SHS-GR11-1 S PREC-111
Week 14: Long Test Long Quiz 2

Use the Binomial Theorem to

expand and simplify the
.
expression .
(3a -4b) 5

Select one·
a. 243a5 - 1·620a4b + 4320a3b2 -
5760a2b8 + 3840ab4 - 1024b5

b. 243a5 - 1620a2b2 + 4320a3b2 +

1

5760a2 b8 + 3840ab3 + 1024b5

,c. 243a5 + 162Oa4b + 432Da2b3 -

5760ab4 + 3840ab4 + 1024b5

d. 243a5 + 16,20a4 b - 4320a3b2 -

57 60a2b8 + 8840ab4 - 1024b5
1

Question 14
Dashboard SHS-GR11 -1S PREC-111
Week 14: Long Test Long Quiz 2

Mark 2.00 out of 2.00

Flag question

Determ ine two coterminal ang les

(one positive and one negative) for
each ang:le.

Select one·
a.
b.

d.
Dashboard SHS-GR11-1 S PREC-111
Week 14: Long Test Long Quiz 2
Complete
Mark 2. 00 out of 2. 00

Use the Binomial Theorem to

expand and srmplify the
express:1on.
(a+ 6) 4

Select one:
a. a 4 + 12a3 + 16a2 + 64a + 12
b. a4 + 4a3 + 36a2 ·+ 144a + 2·16
c. a4 + 24a 3 + 216a 2 + 864a + 1296
d. a4 + 24a3 + 36a2 + 212a + 1290
Dashboard SHS-GR11 -1S PREC-111
Week 14: Long Test Long Quiz 2

Deter,m ine two cotermina l ang les

(one posit ive and one nega,tive) for
each angle.

Select one:
·· · ) 17'n; !___
a.. (. u , 6 , 6

b· . .. · 7rc 2 trr
tl ,- - -
6 I 6

. . 17 7,
,c. u ,- - -
6 ' 6

.•..) -
,·d. . u. .15ir 7
,-
6, ,6

Ques· ion 8
Dashboard SHS-GR11-1 S PREC-111
Week 14: Long Test Long Quiz 2
Mark 3.00 out of 3.00
Fl ag ,question

Find the 1:ength of the arc on a

circ le of radius intercepted by a
central angle '8.
Radius: 3 meters Central
Angle.· 1 rad ian

Answer:
3 meters

Question 10
Gompte e

Mark 1;.00 out of 1.00

Dashboard SHS-GR11 -1S PREC-111
Week 14: Long Test Long Quiz 2

Question 10
Complete
Mark 1.00 out of 1.00

Flag question

Find the sum using the form ulas

for the sums of powers of
[ntegers.

- :- n21
Answer·
91

Question 11
Dashboard SHS-GR11 -1S PREC-111
Week 14: Long Test Long Quiz 2

Mark 2.00 out of 2.00

Flag question

Ca Icu late the binomial· coefficient.

20C1s

Answer:
15,5 04

Ques:ion ·7
Gomp:lete
Mark 2.00 out of 2.00

Flag question
Dashboard SHS-GR11 -1S PREC-111
Week 14: Long Test Long Quiz 2

Calculate the binomial. coefficient.

(85)

Answer.
56

Question 5
Complete

Mark 2.00 out of 2.00

D
Dashboard SHS-GR11 -1S PREC-111
Week 14: Long Test Long Quiz 2

Question 3
Complete
Mark 1:.00 out O'f 1.00

Find the sum using the formu las

for the sums of powers of
integers.

Answer·
979
Dashboard SHS-GR11 -1S PREC-111
Week 14: Long Test Long Quiz 2
G0ll1pi1ete

Mark 2.00 out of 2.00

Flag question

Ca Icu late the binomial· coefficient.

(10098)

Answer:
4 ,950

Ques:jon 12
Gompilete
Mark 2.00 out of 2.00

Flag question
Dashboard SHS-GR11-1 S PREC-111
Week 14: Long Test Long Quiz 2

Use the Binomial Theorem to

expand and sf mplify the
express1 on.

Select one:
a..
1
.rs

b.
1 lOy Sy3 , yl 1,o y
-I -X + yS
xS x• 2X X

1 10)' 5,y y3 Sy"

s - .+ yS
z4 X 2%' X
Dashboard SHS-GR11-1 S PREC-111
Week 14: Long Test Long Quiz 2

Determ ine two coterminal ang les

(one positive and one negative) for
each a ngle .

.., fJ-
u. = -2 1t

Select one:

. ") 2 57r
. 23:n
b. 1( ,U - - -
,2 ' 12

. 36 - 23 -
,c · ll -- - - -
' 2 2
Dashboard SHS-GR11 -1S PREC-111
Week 14: Long Test Long Quiz 2
\. IOOloJ

Question 1.
Complete
Mark 2.00 out of 2.00

Find the tength of the arc on a

circle of radius intercepted by a
central angle 8 1

Radius: 15 inches Central

.Angle: 1ao 0

Answer~
47.12 inches
WEEK 15
 Dashboard SHS-GR11 -1S PREC-111
Week 16: Key Concepts of Circular Functions,
Trigonometric dentities, Inverse Trigonometric Functions
and Polar Coordinate System - Part 005
Short Quiz 13

Find t he exact value o f the

trigonometric function given that
sin u = _!__
13
and cos 11. = - 3 .
5
(Both are in Quad rant IL) Note that
answers in fractions must be
entered like so: 4/5, 1/2, 3/ 4, -
(5/10)

cos (u + v)

Answer.
1·6/65
WEEK 16
Dashboard SHS-GR11 -1S PREC-111
Week 16: Key Concepts of Circular Functions,
Trigonometric !Identities, Inverse Trigonometric Functions
Polar Coordinate System - Part 005
Learn 'ng Activity 13

Mark 1..00 out of 1.00

Flag quest ion

Find the exact value of each

expression.

a ..,CO' (n_;_ n)
-
.3 .

Select one:
l
a.

b.

C.
4G ,111ll 10:22 AM ~ O' 4G1 40% •I ■I

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Dashboard SHS-GRl -1S PREC-1111

Week 16: Key Concepts of Circular Functions,
Tri,g onometric !Identities, Inverse Trigonometric Functions
Polar Coordinate System - Part 005
Learning Activity 13

Find the exact value of the

trigonometrlc function given that
sin u = - 2-
2sand cos v = - ---s
. (Both u and v are in Quadrant Ill.)
Note that answers in fractions
must be entered like so: 4/5, 1/2,.
3/4, -(5/10)

tan (u-v)

Answer.
-(44/117)

Fini~h rPvi,P w
Dashboard SHS-GR11-1S PREC-111
Week 16: Key Concepts of Circular Functions,
Tri,g onometric Identities; Inverse Trigonometric Functions
and Polar Coordinate Syst em - Part 005
Short Quiz 13

Fjnd the exact value of the

trigono,metr1c function given that
smu = -s and cos v = - -3 .
3 S
(Both are in Quadrant IL) Note that
answers in fract ions must be
entered like so: 4/5, 1/2, 3/4,. -
(5/1 O)

sec (v- u)

Answer:
65/56
Dashboard SHS-GR11 -1S PREC-111
Week 16: Key Concepts of Circular Functions,
Tri,g onometric !Identities; Inverse Trigonometric Functions
and Polar Coordinate Syst em - Part 005
Short Quiz 13

Find the exact value of the sine of

the angle by using a sum or
difference formu1a..
105° = 60° + 45°

Select one:
a. sin 105° =

b. sin 105° =

c. sin 1:05° =

d. sin l05° =
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Dashboard SHS-GR11 -1S PREC-1111

Week 16: Key Concepts of Circular Functions,
Trigonometric Identities., Inverse Trigonometric Functions
Polar Coordinate System - Part 005
Learning Activity 13

Question 1
Complete

Mark 1.00 out of 1.00

Write the expression as the sine,

cosine, or tangent of an ang le.

0
Answer: tan 239

Question 2
4G ,11lll 10:22 AM ~ • 4G1 40% •I ■I

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Dashboard SHS-GR11 -1S PREC-111

Week 16: Key Concepts of crrcular Functions,
Trigonometric !Identities, Inverse Trigonometric Functions
Polar Coordinate System - Part 005
Learn 'ng Activity 13
MarK I . OU out Of I . OU

Flag question

Find the exact value of each

expression .
.
a sin 1
1n
- .
rr,. )
3
b· 1.n7-· :ir
6 6

Select one:

a. l

b.. .

e.
Dashboard SHS-GR11 -1S PREC-111
Week 16: Key Concepts of Circular Functions,
Tri,g onometric Identities, Inverse Trigonometric Functions
and Polar Coordinate System - Part 005
Short Quiz 13

Find the exact value of the

trigonometric function given that
.
sm u = -s an d cos v. = - -3 .
13 - 5
(Both are in Quadrant It) Note that
ans·w ers in fractions must be
entered like so: 4/5, 1/2, 3/4, -
(5/10)

tan (u + v)

Answer.
-(63/16)
Dashboard SHS-GR11-1S PREC-111
Week 16: Key Concepts of Circular Functions,
Tri,g onometric Identities, Inverse Trigonometric Functions
and Polar Coordinate Syst em - Part 005
Short Quiz 13

Find the exact value of the tangent

of the angle by using a sum or
difference formula .
285°

Select one:
a. tan 285° =·

b. tan 285° =

d. tan 285° =
Dashboard SHS-GR11 -1S PREC-111
Week 16: Key Concepts of Circular Functions,
Trigonometric !Identities, Inverse Trigonometric Functions
Polar Coordinate System - Part 005
Learn 'ng Activity 13
comp1,ete
Mark 1.00 out of 1.00

Find the exact value of the

trigonometric functi:on given that
. u
sin = ,_ -2S, an d· cos v = - -S,
. (Both u and v are in Quadrant 111.)
Note that answers in fractions
must be entered like so: 4/5, 1/2,
3/4, -(5/1 O)

sec (u + v)

Answer.
5/3
 Dashboard SHS-GR11-1 S PREC-111
Week 17: Key Concepts of Cfrcular Functions. Trigonometric Identities. Inverse Trigonometric
Functions, and Pola r Coord inate System• Part 006
Learning Activ ity 14

Quesfion 3 So!ve each equation for exact solutions over the interval [O.
complete 2n].
Mark 1.00 oot of
1.00 2sinx + 3 = 4
Y Fla,;i
quesllon Select one:
a• { -ll -57-}
,6 ; ,6

b. (!!:}
2

c. £3", Tit}
4 4

d. (i, 53,r}

Quest1on 4 Solve each equation for exact solutions over the interval [O,
Complete 2n).
Mane 1.00 oot of
U)O sinx + 2 =3
'f' Flag
queslion Select one:

a, { -31!' . -7rr}
. 4 ' 4

Finish review

u -
□
WEEK 17 <l O
Dashboard SHS-GR11-1 S PREC-111
\ilfoek 17: Key Concepts of Circular Functions, Trigonometric Identities, Inverse Trig onometric
:Functions., a 11d Pola r Coord inate System • Part 006
Learning Activ ity 14

Q1:1estTon 1' So ve each equation for exact solutions over the i11t1:.rval [O,
Compr@ie 2n].
Marl<: 2.00 oo of
2.00
2 sec x + 1 = sec x + 3
V Fla,;i
question Select one:

a. (!:.J
2

b. (!E, 5" }
3 3
1f Sn
c. [:;' 6}
d. {sn:, 111}
4 4

Question 2 So ve each equatron for exact solutions over the interval [O,
Comprete 2nl
Malik 1.00 out of
1.00 2cotx + 1 = - 1
l" Flag
question Select one:

c. (i's;}
d. {3 rr -, 11}
4 ' 4

Question 3 So ve each equatton for exact soluitjons over the interval [O,
Comprere 2R].
Mai 1.00 out of
1 ,00 Zsinx + 3 =4
Q1:1estTon 5 Solve the equation forexac solutions over the i!"lterval (0,
Compr.ete 2n].
Mark 1.00 out of
1.00 cot3x = {3
'f' Flag
que-s1ion Select one:

1r 7'" l31r 19:n- 2 7r 31 rr}

a.
{
"ii· 18· 18 LB'18.18

Question 6 Give all exact solutions overthe interval [0°, 360,.

Comprete

Mark 1.00 Oil of

sin 0 - sin 20 =O
1.00
Select one;
'f" Fla11
question a.
22.5° + 360° n, 112.5° + 360° n, 202.5° +360° n, 292.5 ° +
b.
11.8° + 360° n, 78.2° + 360° n, 191.8° + 360° n, 2ss.2° + ~
C.

30° + 360° n, 90° + 360° n, 1500 + 360° n, 210° + 360° n, :

where n i, s any Integer.
d.
0° + 360° n, 60° + 360° n, 180° + 360°, 300° + 360° n, whi
G Edimar Agcao1\1 Costates and Roschelle Cons!ant1110 asked to Join ANSWER'S.

Que~ton 7 Give all exact solutions over the interval ;t0°, 360'11.
Comptete
Mark 1.00 out of
4 cos 28 =8 sin fJ cos fJ
1.00
Select one:
"f'Flag
question a.
30° + 360° n, 90° + 360° n, 1500 + 360° n, 210° + 360° n, :
where n fs any integer.
b.
0° + 360° 11, 60° + 360° n, 180° + 360°, 300° + 360° n, whi
c.
11.8° ... 360iJ n, 78.2° + 360° n, 191.8° + 360° n, 258.2° + ~
d.
22.5° + 360° n, 112.5°' + 360° n, 202 .5° +360° n, 292.5° +

Qu~~tlon 8 Solve the equation for -exact solutrons over1he interval fO,
Comprete 21t}.
Ma~ 0.00 011 of
1.00 sin 3x =0
'V Flag
question Select one:

a. I :!!.. 11r l 7r 197T 2 7T ~ }

1 ' 18' I 8' 18 ' 18

Give all exact solutions over the interval [0°. 360°1.

. .
<J O □
fJ i;J G @ ~ @ • Q Q • All All ■ 1 o:52

Questlon '9 Give all exact solutions over1he interval ro0, 3600].
COmJ)let~

Mark 1.00 out of

cos 0 = sin 2 !2
1.00
'f f lag, Select on:e:
<i,ues ion
a.
60° + 360° n, 300° + 360° n, where n is any integer.
b.
70.5° + 360° n, 289.5° + 360° n, where n Is any integer
c.
0° + 360° n, 30° + 360°' n, 150° + 360° n, 1,80° + 360° n, wt
d.
45° + 360° n, 90° + 360° n, 225° + 360° n, 270° + 360° n, v.

Question 10 Give all exact solutions over the interval ro0• 3600].
Co111Pl~e
Mer 0.00 ol!I of
2 - sin 2 0 = 4 sin 2 0
1.00
Sel,ect one:
'f FJa9
question a.
o0 + 360° n; 60° + 360° n, 180° + 360°, 300° + 360° n; whe
b.
11.8° -t 360° n, 78.2° 4 360° n; 191.8° + 360° n, 258.2° + 3 1
c.
30° + 360° n, 90° + 360° n, 150° + 360° n, 210° + 360° n, 2
where n is any integer.
d.
22.5° + 360° n, 112.5° + 3-60° n,. 202.5° +360° n, 292.5° + 3

Finish review

Finish ireview
WEEK 18
j i rc ShortQmz15 X f (2)ANSW£R S x --- ~ I

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..
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-~
JOHN CARLOS MONSERATE ..~ '.

Dashboard SHS.GR11-1S PREC -111 Week 18: Key Concepts ofCircu!ar Fune lions, Trigonometric Identities, Inverse Trigonometric Functions, and Polar Coordinate Sy stem Part 007 ShortOUIZ 15

b.

(o~) (o-~)
. 6 '
'
' 6

'
(./2,8.64),(- ./2, - 0.78).

• d.
I
'
(2 ✓2. 1owH-2 ✓2.1.8s)

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SHS-GR11-1S
Virtual Library

PREC-111
Post Student Concern

Week 18_ Key Concepts of Circular Functions, Trigonometric Identities, Inverse Trigonometric Functions, and Polar Coordinate system Part 007 ShortOuiz 15
·-
JOHN CARLOS MONSERATE ~ •

Oues110n 8 Plot the point giVen in polar coordinates and find two additional polar representations of the point, using -2n c: e < 2n
Complete
(2"2,4.71)
M~r1< 1 OOovtof
,oo
Select one
l'Fla9
question

b.

I
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Dashboard SHS.GR11-1S PREC -111 Week 18: Key Concepts of Circular Functions, Trigonometric Identities, Inverse Trigonometric Functions. and Polar Coordinate System Part 007 ShortOUIZ 15

Find a polar equation of the conic with 1ts focus at the pole
Complete
Conic: Ellipse. Vertex or vertices: (2. 0), ( 10, TT)
Mar1< 1 00outof

"'
'f'Flag
Select one
,0
que,tion • a. r - - -
J+2cos9

b. T-' 1+2cos8 '

C. T-' 1- ~ s 8

d. r--'-
1-sinB

e . T-' 2+s~nfJ

I
Quesb00 8 Plot the point gr.en in polar coordin ates and find two additional polar represen tations of the point using -2TT < 8 < 2TT

"°"""'"
Mar1< 1 00outof
(2'2,4.71)

Select one
'f'Flag
~ue•tion

~i (-•-~)
( 4' 3 . ' 3

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Week 18. Key Concepts of Circular Functions, Trigonometric Identities, Inverse Tngonomellic Functions, and Polar coordinate s ystem Part 007
-
JOHN CARLOS MONSERATE , ~ '

Short Quiz 15
* !

auestKln 6 Find a polar equation of the conic with its focus at the pole
Complete
Conie• ParaOOla, Vertex or vertices (5, TT)
Mar1< 1 00001of
, oo
Select one:
l'Flag
questiorl a. r -3+2cosli
-"-

b. T = 1-s~nli
c. r = - ' -
1+2cosli

d r= - ' -
. 2+slnfJ

,0
• e . T-' 1-cos8

'

I
t. r= 1-cos-8

Quesoon 7 Find a polar equation of the conic with its focus at the pole.
Complete
Conic : Ellipse, Vertex or vertices (2, 0), (10, TT)
Mal1< 1.00 outof
, oo
Select one
'f'Flag
,0
question
• a. T = 3+2cos9

b r= - '-
. 1+2cos8

c. r= t-~s9

d. r = - ' -
1-sm8

e. T = 2+s~n9

t.r=-"-
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Dashboard SHS.GR11-1S PREC -111 Week 18: Key Concepts of Circular Fune lions. Trigonometric Identities, Inverse Trigonometric Functions, and Polar Coordinate System Part 007 ShortOUIZ 15

auestion 5 Find a polar equation of the conic with its focus at the pole
Complete
Conk: Hyperbola Eccentrieity: e"' 2, Directrix- x"' 1
Ma~ 1 D00<11ol
, oo
l"Flag
question
Select one

,1 _ r
.
= l+2cos8
b. r= - ' -
1-si nB

c. r = - ' -
t-cos 8

I
~. r =-"-
1-cose

tr=-'-
. 1+2 cos 8

Ounc.on 6 Find a polar equat10n of the conic with its focus at the pole
Complete
Come: Parabola, Vertex or vertices (5, rr)
M1~ 1 D0outof
, oo
Select one:
l"Flag
question
a. r = l+21:os 8
b. r = l-s~n8
c. r = - ' -
1+2cos 6

e. r = t - ~:se
t.r=-'-
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Week 18. Key Concepts of Circu!ar Functions, Trigonometric Identities, Inverse Tngonometrie Functions, and Polar coordinate s ystem Part 007
-
JOHN CARLOS MONSERATE , ~ '

Short Quiz 15
* !

Ouesc.on 4 Find a polar equat10n of the conic with its focus at the pole
Complete
Come: Parabola, Eccentricity: e"' 1 Directrix: x"' -1
Ma~ 1 000<11of
, oo
Select one

"'"'
question a. r=-'°-
t-cos8

b. r = - ' - ' -
H2cos 8
,
c. r

f. T
.
= 1+2cos8
r= - ' -

r=-'-

=
2+sln8

1-cos e

l-;n8
I
Ouesoon 5 Find a polar equat10n or the conic with 1ts focus at the pole
Complete
Conk Hyperbola Eccentr1eIty e: 2, Directnx: x: 1

Select one·
l"Flag
qoen10n 3. r=-"-
. l +2cos8

b. r = - ' -
1-si nB

c. 7 = 1-c~s8
d. r '
= 2+sln8
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Dashboard SHS.GR11 -1S PREC -111 Week 18: Key Concepts of Circular Functions, Trigonometric Identities, Inverse Trigonometric Functions. and Polar Coordinate System Part 007 ShortOUIZ 15

Ouesoon 2 convert the polar equation to rectangular form

Complete
Mar1< 1 00outof
r2 = cos8
, oo
Select one:
l'Flao

I
quutlon a..X 2 +4y-4" 0
b. 4x 2 - sy 2 -3sy- 36" o

c. (x2 + y2)2 "' sx2y - Zyl

d.y '"4
• e.x2 +y2- xm:o

Ouesoon 3 Convert the polar equation to rectangular form

Complete
T ; -'-
Mar1< 1 00ootof l+si n9
, oo
l'Flllo Select one:
quesuon a.. (x2 + y2)2 ,, sx2y _ 2yl

b. 4x 2 - sy2-3sy-36"' o
• c. X2 +4y-4"' 0
d. x2+y2-xm ,,,o

e.y =4

Ouesoon 4 Find a polar equation of the conic with 1ts focus at the pole
Complete
Conic: Parabola, Eccen!Jicity: e"' 1, Directrtx:: x"' .1
Mar1<100outof
, oo
Select one
l'FlaO
question a. r : - " -
1-cos8

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.
Dashboard SHS-GR11-1S PREC-111 Week 18. Key Concepts ofCircu!ar Functions, Trigonometric Identities, Inverse Tngonomellic Functions, and Polar coordinate system Part 007 Short Quiz 15

FiniSh review Ouesoon 1 PIOt the point given in polar coordinates and find two additional polar representations of the point, using -2TT < e < 2TT
eoo,,,...
(4, - i)
Mart 1 000\llof

l'FIIIO Select one

question

1
(,¥),(-,.-¥)

b.

(✓2,8.64).(- ✓2, - 0.78)

 Find a polar equation of the conic with its focus at the pole.
Conic: Ellipse. Vertex or vertices: (2, 0), (10, rr)

Select one:

a. r ~ i+z:o,s
b. '-0-
r= -J-+Jco.sS
t
c.r • - -.-
1+.in ,

d. r;_t_O_
t- cos8

e . r • -1-
1- coss
2
f. r • - -. -
1- 11nfJ

Convert the rectangular ""'ation to polar lorm Assume a > 0

3x - y+2 = 0

Select ooe:
•. r 2 a 16secBcscBM32cK28
b. r a 2acos8
c. r =a
2
d. r • ---- --
Jcos f-·sin 6
4
e. r - - - or - - •-
1- ros I ucos 9

Convert the polar equaboo to rectangular form.

r =4

Select ooe
a. X' • v' • 16
b. X2 ♦ y1 + 2y■O

c• ..f!.x +y=O

d. X2 ty' - 4y •0

Fm a polar equation ol the eonoc v.th Its locus at the pole.

Conic Parabola Eccentricity: e = 1 Directrix: x = -t

Select 008
a. r • -1-
J. ♦ tln f

b. r•--'0-
J•lcotl
2
c. r • - - -
1+zcos1
2
d. r • --
1- 11"'

e. r• -1-
1- c0t:I

f. r = ---1L.
I-COIi

Solve each equation lor exact solutions over the inleMI [o". 360°1
(cot8 - "3)(2 si118 + "3) = 0
Select ooe.
a. {90°, 21 o0, 330"}
b. {300. 210•, 2400, 300o}
c. {15°, 130°, 430"}
d. {0°, 45°, 22s0}
e. {30°, 200°, 310"}
 Solve each equation for exact solutions over the intervaJ (00, 360°].
(tan 9 - l)(cos9 - 1) = 0

Select one:
a. {30°, 210•, 240°, 30o'}
b. 1so•, 210°, 330•>
c. {o', 45°, 225°}
d . {30°, 200°, 310°)
e. 11s•, 130•, 430°}

Solve lhe equahon for exact scM,ons over lhe interval (0 2TT)

tan 4x • 0

Select one

0
• • 3• 11 s.. 3,r 711}
•. { • 4 ' 2 ' 4 ' ' 4 ' 2' 4

G.ve all exact solutions over lhe ,nler,al (0 360 J

1 - sin8 = cos 29
Selecl one:
•· 7O.S0 + 360° n, 289.S0 + 360° n, where n Is any lntecer
b. 00 + 360° n, 30' + 360' n, 150° + 360" n, 1so• + 360° n, where n Is a ny Integer.

c. 60° + 360" n, 300° + 360° n, where n Is any integer.

d. 45° + 360" n, 90• + 360° n, 22s• + 360' n, 270° + 360° n, where n is any integer.

Convert lhe polar equal<cn lo reelangular fcnn.

r - 2 sin 36

Selecl one
a. (x2 + y2)' • 6x2y -'tof'
b. X2 + 4y- 4 • 0
c.y=4

d. X2 •r -•"' = 0
e. 4x2 - 5,r - 36y - 36 = o

Convert lhe polar equation lo reclangular form

r = 4csc8
Select one
a.X2 +y'- x"'•0
b. X' • 4y - 4 = 0
c. (x2 • y')2 • 6x'y -2v'
d. y =4
e. 4x2 -5y'-36y-36 = O
Plot the point given in polar coordinates and find two additionaJpolar representations of the poinl using -2n < 8 < 2TT.
(2 ./2, 4.71)

Select one:

a.

•
( ./i.M4), (- ./i. - 0,78)

'
b.

..
(2./i. 10.9!1~(-2./i.7.85)

ldenlofy lhe conic of r • -2- eo1•

•-

Answer: e l ipse

Conver1 the polar equation to rectangular form.

6
r = 2- h l n 8'

:select c,ne:
a. (x2 • y2 )2 = 6x2y - 2y'
b. X2 + 4y - 4 = 0
c. p4
d . 4X2 -5y 2 - 36y - .l6 = 0

e. x2 + y2 -x2i-s = o

Solve lhe equabon lot exact solutions o,,,, lhe interval {O 2rr].

cos2r =_.!.2
~ed ooe.

b. { ,r .!..!.! 13,r 23,r}

12· 12' 12 ' 12

f • ,r 31r Sir 3tr 7•}

e. l O 7·T·7·"· 4 • 2 · ,
 Solve the equation for exact solutions over the interJal (0. 2rr) .

./2 cos 2x = -1
Setect one:

a. {3,r 5,r ~ 13,r}

8' 8' 8 ' 8

d { ,r 7,r 13,r 19,r 25,r 31,r}

. 18' 18' 18 . 18' 18' 18

Find the exact value of lhe cosine of the angle by using a sum Of difference formula
195' = 225' - 30'

Select one

a. cos 195° = -:? (./:1 I)

b. cos 195° = ./z ( I - .J:1)

4

c. cos 195°=- ./2{./J + 1)

4

d. cos 195° = ,/2( .fi + 1)

4
Solve the equation for exact solutions over the inteival (0. 2rr].

cot 3x = ,/3

Selecl one:

a. {3,r 5,r !!_! 13,r}

8' 8' 8 ' 8

b { ,r 7,r 13,r 19,r 25,r 31,r}

18' 18' 18' 18 . 18' 18

d { ff 5,r 13,r 17,r}

iYii·12·12
,r 7,r 13,r 19,r 25,r 3 I"}
•. { 18'J8'18'18'18' t t
 Give all exact solutions over the interval (0°, 360°).

sin 6 - s in 26 =0
Select one:

•· o• + 360° n, 60° + 360° n, 180° + 360°, 300° + 360° n, where n Is any Integer.
b. 22.5° + 360° n, 11 2.5° + 360" n, 202.5° +360° n, 292.5° + 360" n, where n is any integer.
c. 30° + 360° n, 90° + 360° n, 150° + 360° n, 210° + 360° n, 270° + 360° n, 330° + 360° n,
where n is any integer.

d. 11.8° + 360° n, 78.2° + 360° n, 191.8° + 360° n, 258.2° + 360" n, where n Is any integer.

Give all excel solutions ever the inlerval (0°, 360°'].

cos8 = sln 1 !2

Select one:
a. 10.S0 + 3603 n, 2&9.S0 + 360' n, where n is ;any integer

b. 45' + 360° n. 90° + 360° n. 22s• + 360° n. 210• + 360' n. where n isanv Integer.
c. o0 +- 350• n, 30° + 360c n, 1so0 + 360° n, 1ao• + 360° n, where n 1s any lnteser.
d. 00° + 3G0° n, 300° -t 3G0~ n , where n i.si)ny integer.

Give all ex~ t solulion-s O\'er h e nterval (O', 3€0°)

2 cos• 20 = 1 - co• 20

•. 30° + 360" n. 90° + 360° n, 150° - 360' n, 210• • 360' n, 270° • 360' n, 330° • 360' n,
where n is any integer.
b. o0 -1- 360c n, 6<:f> + 360° n, 18~ + 360°, 300° -1- 360° n, where n l!i onv Jn.tcger.

c. 11.s• + 360° n, 78.2' + 360' n. 191.8° + 360" n, 258.2° + 360° n, where n ls any Integer.
a. zz.s• - 360' n, 112.5° + 360° n, 202.5' +360' n, 292.5° + 360° n, where n Is any integer.

Determine all solutions of each equation in radians (for x) or degrees (for 8) to the nearest tenth as appropriate.

3sin 2 x - s inx-l =0
~eel one:
a ••9 + 2nn, 2.:3 + 2nTT= 3.6 + 2nn, 5.8 + 2nn, where n is any integer

b. !!: + 2nn, ~ + n, ~ + 2nn, ~ + 2nn where n is any integer

3 l 3 l

c. !!: + 2nn, !!!: + 2mr, ~ + 2nn, !!!: + 2mr where n is any integer
3 l 3 3
d. 1 + n , 2.3 + 2nn, 3.3 . 2nn, 5.8 + 2nrr= where n is any in1eger

•· i + 2nn, ir + 2nn, ¥- + 2nir, where n Is any Integer

Solve the equation for exact solutions over the inteival (0, 2rr).

2v'3sin2x = ,/J

Select one:

a. {37,-8' 5w8. !.!..:!!'

8 . 8
131r}

d { 1r 71r 13.,, 1971' 25,r 311r}

. 18' 18' 18' 18' 18 ' 18

Conver1 the po:Jar equation to rectangular form.

r 2 =cos B

Select one:
a. X2 + 4y - 4 = 0
b. (x2 • y2 )' = 6x2y-2y'
c. y = 4
d. 4x2 - 5y2 - 36y - 36 = 0
e. X2 + y2 - x21-s = o

Comer1 the rectangul ar equation to polar form. Assume a > 0.

f - 3x - 16 = O

Select one:
a. r= 2acos 8
b. r - -2
lcosi- s:in9
c. r =a
d. r 2 = 16sec 8 csc 8 =32csc2 8
4
e. r = -1- cos9
- or - -ltcos9
•-

Find the exact value of the trigonometric function given that sin 1l = i, and cos v = - ! . 180th are in Quadrant IL) Note that answers in fractions must be ente·ed like so: 415. 1,'2,
13 S
3/4. -{5110)

sin (u+v)

Answer: -{63/65)

Convert Ile polar equation to rectangular form

-2 -9
r =1uln

Select one:
a. (x2 • y')' = 6x'y - 1y'
b. 4x2 - 5y2 - 36y - 36 = 0
c. X2 + 4y - 4 = 0
d. X2 + y2 - x2" = O

e. y=4
1/lhite the expression as the sine, cosine. or tangent of an angle.
u n2x+ tan .:r
1-tan2x t anx

Answer: tan 3x

Find the e>:act value of the cosine oflhe ang.e by using a sum or difference forn1ula
195' = 225' . 30'

Select one

a. cos195°= -12(, _ JJ)

4

b. cos 195°= - -l/(JJ - 1)

c. cos195°= - ✓2(✓3 + 1)
4

d. cos 195'= ✓2( ✓3 + 1)

4

Firn.J d µ l ld l t::\1Ud iu11 u f Ult: 1.,'\llli(.; wilh ii:::; ru,i,;u:::; a l U1t: !Joi'=,

Conic: Parabola, Vertex or vertices: (5, rr)

Select ore:
1
ca. r • - -
H•in,
,.
b , r = l♦2<o.s8

d . r:. - 1-0 -
t - t0f8
2
e. r~ i+2<o•8

2
f. r • - -. -
1 - 11118

GI\e all exac1scdu1Ions , ver the Irteiva lt.:0, JO:f i

sll1 zo = z cos• o

Sclcc: ooc:
a, 70.S' + 3603 n. 289.S0 + 360a n, where n is ~n·, inteeer

h o0 + 360c n, 30n+ 360' r,, :tSOO + 36<>° n, 180°+ 360° n 1 where ri iso,ny lnttger.
11 1
c, 60 -t 35d' 11, 300' + 360 n, where n is any integer.

a. 45' t 360° n, 90° + 360° n, 225° t 360° n, 270' t 360° n, where n is any Integer.

=ind the exa:t v aJoe ~ the l ¥19e,t oi the anfle bf using ;i ~um or dfference fomiola.

Sdt,1,;l 011e.

a.tan (-165i° = ./2(1 - ./3)

4

b. ton (-•1651°- - jz(./i - 1)

4
 Conver1 the recianguJar equation to polar form. Assume a> 0.
xy = 16

Select one:
4
a. r = -1- cosS
- or - - •-
1+oos9
b. r =a
2
c. r ; - --- - -
3co1 B•sinB
d. r 2 = l6sec 8 csc 8 = 32csc2 8
e. r = 2acos 8

Find the exact value of the trigonometric functionQiven tt at sin u = -fs and cos v o -i.(Both u andv are in Quadranl Ill.) f\ote that answers in fractions rrust be entered like so:
415, 1/2, 314. -(S/10)

t,;~ (u ... v)

Answer: 315

Sol,e each eqJation for exact solutions over the interval (00, 360°].

2 sin0 -1 = c sc O
Select one:
Q , {o', •s<, 225°}
b. {30°, 210•, 240°, 300")
c. {30°, 200•, 310°)
d. 1so•, 210°, 330•1
e. 11s•, 1io•, 430°)

Find the exact vaJue of each expression.

a. cos(120• + 4S' ) b. cos120 • + cos4S•

Select one

.Ji - ./6 ✓2-1 1

• . (1) (b)
4 2
h ...,() (l,)
,/j
b. 'ca)
4 2

c. (a)
I - JI - I
(b)--2-
2
d, 'ta) h ./6 lb)
I+ h
4 2

Give all exact solltions O\'er the irterval (06, 36~°').

4 cos 29 = 8 sln9 cos9

5elcd ooe:
a. o0 • 360° n, 60>• 360• n, 180° • 36cf, 300° + 360° n, whe re n is any Integer.

b. 30° • 360° n, 90° + 360° n. 150° • 360° n, 210° • 360° n, 270° • 360° n, 330° + 360° n,
where n i s any integer .

c. 22.5° + 360' n, 11 2.5° + 36o" n, 202.5° +360° n, 292.5°+ 350" n, where n is any integer.
d. 11.8° • 36d' n, 78.2° • 360° n, 191.8' • 360' n, 2ss.2° • 360" n, where n Is any Integer.
Convert the recianguJar equation to polar form. Assume a > 0.
x2 + y2 -2ax= O

Select one:
a. r= 2acos 8
b. r~- ---1- -
J cos 9 - ,:in 9

c. r =a
d. r 2 == l6sec 8 csc 8 == 32csc2 8
4
e. r = -1- cos8
- or - - •-
1+00s9

)etE-rmine a l solutio,-s ol e ach e:iuafon in radians (for x ) or degrees (for 8) to the nea·est tent , as appropriate.

4cos 7 x-1 == 0

5elect ooe:

•· f + 2111r, 11 + z n.,, ¥+ 2111r, where n ts a11y I nteg er

*
b. i + 2111r. 7+ 2111r. 7+ 21ur. + 2mr where n is a ny i n t eger
c ..!, + inn, l .J + lnTT= u; + inrr, t,,H +lnr, wneren 1s an'j integer

d. ; + 2rur, 7+ n,!!f + 2nn,~ + 2-n n where n is any integ er

c.1 • '"= 2.3 , 2nw, 3 .3 · 2nrr, S.8 • 2n1t, where n is any intcgcf'

Convert the recianguJar equation to polar form• .Ossume a > 0.

y=4

Select c,ne:
a. R=4
b. R=3sec8
c. R=4csc 8
d. R=6

Corwert the polar equation to rectangLlar f'orm.

r=-- •-
2- h"!n t

Select ooe:
a. X' + -'y-4= 0
b. Xl + y2 -.c213 = 0
c. (x2 + .,2,2 = 6>.2v - 2v3
d. 4lc2 -5y2 -36\,-36 =O
e . y - ,t

Convert the recianguJar equation to polar form. Assume a > 0.

xy = 16

Select one:
a. r ~ -l
lco.19- sin9
4
b. r = -1- cos8
- or - - •-
1+00s9
c.
d. r 2 == 16 sec8 csc 8 == 32 csc2 8
e. r == 2acos l/
Find a polar equation of the conic with its focus at the pole.
Conic: Parabola, Vertex or vertices: (1, -nJ2)

Select one:
a. r:. _,_o_
1- cosS
b.
l
c. r • - -. -
2+•1n ,
2
d. r • - -. -
1-11n 9

10
e. r ~ - - -
J ♦ 2c.oa8

1
f. r • - -
1- cosl

, __,_
Convef1 the polar equation to rectangular form

1tlln 61

Select one:
a. x2 • 4y - • • o
b. 4x2 -5y2-36y-36 =O

c. y =4
d. X2 •r - x"'• O
e. (x2 • r'i' = 6x2 y - 2-y'

Conver1 the colar eciuaton to reclanaular fcrm.

T = 2sln38
St:lt:(.;l om::.
~. y = 4
b . x2 + y 2- xm =0
c. 4x2 - 5y2 - 36y - 36 = 0
d. X2 + 4'/ -4= O

e. I•' + y')2 = 6x2y - 2y'

Gove all exact solutions over the interval [0° 36o']

4cos29 = 8sln9cos9
Select one

•· 11.s• + 360° n, 78.2' + 360' n, 191.8° + 360" n, 258.2° + 360° n, where n Is any Integer.
b. o• + 360° n, 60° + 360° n, 180" + 360", 300° + 360° n, where n Is any l nteaer.
c. 30° + 360° n. 90° + 360° n. 150° + 360" n, 210° + 360° n. 270' + 360° n. 330° + 360° n.•
where n is any inteaer.
d. 22.s• + 360" n. 112.s• + 360° n, 202.s• +360° n. 292.5° + 360° n. where n Is any Integer.

Solve each equation for exact sohsfions over the interval (00, 360'1
(tan9 -1)(cos9 -1) = 0

Select one
a. (90°, 21 00, 330°)
b. {30". 2100, 240', 300'}
c. (15", 130°, 430°)
d. (30", 2000, 310'}
•. {o", 45", 225°)
 Solve each equation for exact solutions over the interva1 (00, 360°].

( cot 8 - ./3)(2 sin 8 + ./3) =0

Select one:
a. {90°, 210°, 330°)
b . {0°, 45°, 225°)
c. {15°, 130°, 430°)
d. {30°, 200°, 3 10°)
e. {Jo•, 210°, 240•, Joo"J

~nlVP. thi=- P.rp .:itinn for P.·<.:ici J=:nl1rtinn.c:: OJP.r thP. infP.v;li (0 "1']

cos2x = !'.2'.?:

Seleci ore:

b. {'"
2' 6' 6
7., 11..-}

d.
..
Solve the equation for exact solutiollS JVer the i"lfervzl {C. 2rr].

cos 2.x=-!.2

•.{"! ~ 13,r 2311'}

12' 12' 12 ' 12

o .,, 11 3,, s,,. 3,, 1.,,.}

c. { • 4 ·?· ◄· 11·7·2·7

Find• polar equa!lcn of the conoc ••th Its rocus at the pole
Coroc Ellipse \leftex0< vertices (2 0), (10. n)

Select one·
l
a. r •~

c. r•-•-
l - ainl

d. r = -•O_
1- totl
1
e. r • 1+2c:osl
-- -
1
f. r • - -
2+.,nl
Convert the polar equation to rectangular form.
r =4

Select one:
a. X2+y1 - 4ysQ

b. xi+v1+ 2y;0

c. .J3x +y=O
d. X' •y'• 16

Give all exact solu1ons over the interval (0°, 360°).

sin 8 - sin 28 =0

Select one:
a. 22.s• + 360° n, 11 2.s• + 3600 n, 202.5° +360° n, 292.5° + 3600 n, where n is any integer.
b. 30° + 360° n, 90° + 360° n, 150° + 360° n, 210° + 360° n, 270° + 360° n, 330° + 360° n,
where n is any integer.

c. o• + 360' n, 60° + 360° n, 1800 + 360°, 300° + 360° n, where n Is any Integer.
d. 11.s • + 350° n, 78.2° + 360° n, 191.8° + 360° n, 258.2° + 360° n, where n Is any Integer.

Cetermine all solutions of e ach equati on in radians (for x1or degrees (for 8) tc the nearest tenth as appropriate.

2 cos 1 x+cosx = 1

Select one:
a. !
3
+ 2mr, !!!l + 2nn, ~
3
+ 2mr, !!!
3
+ 2nn where n is any inte9er
b. i + 2mr, ,r + 2nrr, ~ + 2n,r, where n is any lnte9er
c. 1 + TTi 2.3 + 2mr1 3.3 . 2nn1 5.8 + 2nn, wfl.ere n s any integer

d. i+ 2n1r,7+ n.~ + 2nn,7 +2nn wh.ere n.is any integer

Convert the polar equation to rectangular fonn.

r = 4cscfl
Select one.
a.X2 +'4y-4=0

b. 4x1 -5y'-36y-36=0
c. (x2 + y2)' = 6x2y - 2'f'
d. y =4
e. X2+y2 - x213 =0

Determine all solutions of each equation in radians (for x) or degrees {for 5) to the nearest lenth as appropnate.

4 cos 2 x - l =O
Seled one
a. 1 + n 1 2.3 + 2nn, 3.3. 2nn. 5.8 + 2nn, where n 1s any integer

b ..9 + 2nn1 2.3 + 2nn, 3.6 + 2nn, 5.8 + 2nn1 where n is any integer

c. ; + 2n,r, ~ + 2n,r, ~ + 2n11)f + 2n,r where n is any inteoer

d. i + 2n,r,,r + 2nrr, ~ + 2nrr, where n Is any Integer
e. i + 2mr, ~ + n/f + 2nn. ~ + 2n,r where n is any inteoer
 Find a polar equation of the conic with its focus at the pole.
Conic: Parabola, Vertex or vertices: (5, rr)

Select one:
1
a. r • - -
2+.in ,
1
b. r= - •-
1-cotB

c. r ~
1
1+2 :0,8

d. r = 1+2:0•8
2
e. r• - -
1- ain8
1
f. r • - -
1- cosl

Convert the rectanguJar equation to polar form As.smie a> 0.

x' +y-.2ax•0

Select one
a. r 2 ; 16sec9csc8; 32csc28
b. r - Cl

c. r • 2acos9
2
d. r = - ---- -
3C'DJl• t1t1I

e. r ; - •- or - -t +cosl
•-
1- cosB

2
Identify the conic of r• - -
z .. cc,s •

Answer: Ellipse

Vt\ite the expression as l'le sine, cosine or tangent of an angle

UJl1l' t taAX
1-u.a.2xta.11x

Answer: tan 3x

Convert tie Polar equat,on to rectangular form

r 1 =cosB

Select one:
a.y•4
b. 4x2 -5y'-36y-36 = 0

c. x 2 • 4y- 4 = o
d.X1+y2 - x213 •0
e . (x2 • y')' = 6x2y - 2y'
Find the exact value of the cosine of the angle by using a sum or difference formula.
195' = 225' . 30'

Select one:

a.cos195°= ✓2( 1 _ JJ)

4

b. cos 195' = - ..!;c ./3 - 1)

c. cos 195°= J2(J3 + 1)
4

d. cos 195° =- ✓2( ✓J + 1)

4

SOMO the equation for exact sokmns over the inte,val (0 2nj

cot 3x • ,/'j

Seledooe:

e. { 0 - -
,, Ztr
-
4,r 511}
• 3 ' 3 ' "· ·' ' 3

Give all exact solutions over the interval (0°, 360°'].

sin 28 = 2 cos 2 9
Select one:
a. 60° + 360" n, 300° + 360° n, where n is any integer.
b. o• + 360° n, 30° + 360' n, lSo" + 360" n, 180° + 360° n, where n Is any Integer.
c. 70.5° + 360° n, 289.5° + 360° n, where n is any integer

d. 45° + 360° n, 90° + 360° n, 225° + 360" n, 270° + 360° n, where n is any integer.

Coroer1 the 1eciangular equaton t,, poar form. O.ssume a> 0.

y:4

Select one:
a. R=4
b. H = :Ssectl
c. R=4csc 8
d. A = 6
 a..--. 4 Findthetengtllofthearcoo a Clfdeof•adiusl'llercefAe<lb'facentralangle8
Radius3meters Central Angle 1 radian

Delefl'nine two cote11TW1al angles (one posrwe and one negative) for each angle

1.9• ~

s./e d -

a. (i)!f".- T

Use the Bn;imal Theorem to expand m ~ the e.>llfCSSIOrl

--
(J.a . 4b'f'

a . 215a5 .1s20a"b + 2320a3b1 + E760aztJi. 3840ab' - 5344b5

b. 115a5 + 1620a"b . 4320a3b1 .576Qa2b3 + 3840ab' - 1024b5
c. 2~5 - 1620a"b + 4320a3b1. 5760rtr + 3840ab' . 1024bs
d. 24381 + 1620a'b • 4320a3b1 • Ui40a2tr + 3230ab' . 1024bs

7
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a..-- 7 Comerl lhe redar191A• equation to pobr form. Assume a > 0

Jx . y• 2 • 0

a. r "" JCN;:11111,
b. r • 2a cos 8

1
_;,.,or-
d. r- a

o.--. 8 Chooseane:,iprC$$100 for the<1pparentnthlcrmofthe~ Assumetllaln~with 1

1+ ¼-¼•-!.•ii• ·"
~ seledone

.. '

d. "•
(
..,
l )"(Jt ♦ I)

a.-- 9 Calcl.laie the blrlomal coefk:lenl

~ ..
Dashboard SHS-GRll-1S PREC-111 'Neel: 20 Second Quarter Exam Second Ouarler Exam

a,

....
d.

o.-9 Cakuate lhebmomalcoefflcient

Answer: !i6

Choose an expresSIOO for lhe appareril nth lemi of lhe :sequence Asstane that n begals with 1
1 l 4 S i
t· i ·i·7·9· ...
,. r-v Select one
C 1)111tl)

b . ._
,.." '
( I)'" '

d. -., It!
I
e. ~ ,r

Nextl)a9" ►

~ - ..u • • " - ' - - ~ " ' - " ' - - C ~ ~ - • •

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1~1~ ;0~7 ~
"'""""' SHS-GR11-1S PREC-111 'Neel: 20 Second Quarter Exam Second Ouarler Exam

QUIZ NAVIGATION ~ 11 Solve eadl equation for exact solutions over Ille irller.al [Cl°. 3601

CYREL JIJUAN PIU

~~~---~~~
~~;~;~~
~, .. --
(tiln8- l )(cos8-1) • 0

a.{JOll,20(/J,310°}
b.{l<f, 21o",24(111,JOO°}
c.{o",4s11, 22!i°)

;~;~;;; d.{9(JI>, 21o0, Jlll°}

e. {1S4,130°,-430°}
i ;~;; ;;
;;;;;~; ~ ,, Faldlhesum.

;;;;;; ~, ..
I:! . ,(k + 1)1 (k - 3)

Show al qoesboos on ooe page Answer: 88

'"""'~

Answer: 30

o.-- 14 Solve each equ.tllon faexad:solubonsover lhe 111terval [o0. 360°!

2sln8- t • cscB

I I I I.(~

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Sol\'eeactiequatiooforexactsolulionsoverlheil11er.al [OO. 3601

--
2sin8 - t = csc8

a . {Jdl, 21o0,24QO, ~
b.{go0, 21oO, JJOO}
c.{30°,20()0, J1o0}
d.{<fl,45°, 22st')
e. {1fi11, 1:io<', 4JOO}

Delefrnirle two cotermnal angles (one posrtNe and one negative) for each angle

-- a. (ii)~-~

Calwai.e lhe bmomal coellaent

Answer: 15504
Dashboard SHS-GRll-1S PREC-111 'Neel: 20 Second Quarter Exam Second Ouarler Exam

Choose an expressioo for the app.arenl nth term dlhe sequence Assume that n begins with 1
-J J -• 5 -6
_,oo ....a1
•m

--
]•4·5·6·7•"""

a. •. ( •r·•
b. "• ~

d. ._ I•!
.. (
..,
l)"(it ♦ I)

ldenllfylheconic of r • _.:,.,
2

Answer: el1pse

Find a fomiola for Ile sum oflle fifstnlefms oflhe sequence

~n.,
- serectone

a. S,,• (ot: 1)

b. S.,• Z(1t,.· l)

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Find a formula for Ile sum oflle kstntem"JS dlhe sequence

c . S,, a (ft•I )

'Nrile lhe expreMionaslle sine.cosinoe ortafl9Ml d anaogle

Slll3COS 1.2 - cos3 sin 12
_,oo ....a1
..
-
'oo Answer SIil 1.8
~,

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"'""""' SHS-GR11-1S PREC-111 'Neel: 20 Second Quarter Exam

~ 21
Second Ouarler Exam

QUIZ NAVIGATK>N Find aformuta for lhe sum oflle fintl= oflhe $eQUel'ICC
1 S 9 . 13

..
__;;;;; -
CYREL JUUAN PILI
~, s.i.a-
a. S,• n(l n • l)

b. S. • (ln• 1)

~~~~;~~
c. S,,•(2n + l )

d. S. • n(ln + 1)
~ ~iH; '-'-'-'-
1;;;;~; ~ 22
;;;;;~
Fnllhewm

r:.,11;.1.,
Show al quesbom on one paoe
Fn shrewM
~, .. Ans'M':I'": 9J5

Answer: 30

Findlhelenqtl'l d lhearcon a ardeof ·adius 1 1 1 ~ t,,- acentral angle e

Central/vqe lsdl

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Find the exaict vaiue of the mgonometri: l\.lncliongiven llatsm and cos v• -i. {Both u and v are in Quadrant Ill ) Note ltlatanswers III fractions rrustbeentered lke so· 4/S 112

314 ,(5110)

cos(u•v)

Find the exact v-..e of the tangent of !tie angle 't1f uwig a sum or difference fomua

--
- 165°

. . ... ,.16'r •

b.1'n(-1661'•-4(✓J + 1)

,.un(-16'r •
4 (.r, ,)

4(, _J,)
I
d.tan(-166)0 • 2 ./3

Plot the point 9IVefl in poiar coor<inate~ and find two ilddibonal polar represeotafioos of lie poinl using -21'1 < e < 2rr

(0, - ~ )
Dashboard SHS-GRll-1S PREC-111 'Neel: 20 Second Quarter Exam Second Ouarler Exam

Convert lhe red~ar eq.iaboo to polar form Assume a > 0

x2 + f - 2ax • 0

,_;,.,or -
b. r = Jao,o ;~a nf
c. r - Zacas l
d. ,.2 • 16 sec i utlil • ]2UCZ8

Determine al soluboos °' each equatiol 111 r~ns (for x} or degees (for 8} lo the nearest tenltl as appropnate

--
2cos:l x+cosx=l

a .1 • Tl, 2.3 • 2nTI, 3.3 - 2nlT, 5.8• 2nTI, where n is any integer

b. i + 2n'lf.7 + If,~ + 2u,7 + 2nrt where nisa.ny integer

c ••9 + 2nlT, 2.3 + 2nlT, 3.6 + 2nlT, 5.8 + 2nTI, whef'e n is any intege,r

i + 2n'lf,~ + 2nlf,~+ ZM,~ + Znlf whn-t n ts a.nyinUgtr

I
d.

e. i + 2n'lf,1C + 2nlf,~ + 2n11, whert n ts any tnttgtr

Use lhe Btnomal Theorem lo expand m ~ lhe expre$$!0n
2(x-3f +S{x- 3'f

s.!ed=
a.2x'-12x'- 96x2 + 232x +207
b. 211• . 24x3 + 113x2 • 246x + '107

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Ql.z: NAVIGAOON Expand lhe bloomal by USlf'l9 Pascal's Tnangle to oetemline lhe coeffiaeflts

(2t- sl'
CYREL JUUANP1U

-- a .32t'-sor'.. +80t312.40t213+ 10t1•-•5

b. 32t5 - 80t41 + .wt3st + 8()t21 3 + 20ts• . 1S

c.32t' - 20n+40t3s 2 -'40t2s 3 + 10t1' -15

d. 16t'+40t'1+80t3s 2 . 8()t2s 3+Hlt1' - •s

~ ,, Use lhe Btnomal Theorem lo expand m ~ the expre$$!0n

(3a - 4o'f

F--
s.!ed=
St.ow al qoesooos on ooe page a. 243a5 + 162'0INI. 4320a3bl - !760a2b3 + 3840ab' -1024b5
b. 24~ • 1620a"t> • 432037b3 - S760ab' • 3840ab' • 102'">5
c. 20a5 - 1620a2b1 • 4320rb1 • 5760a2b 3 • 3840ab3 • 1024b5
d. 243a5 - 1620a"b + 43'10a3trl - i760a2lY + 3840ab' - 1024b5

~ ,, SOive the equation for exact solul!Oll$ ever lhe 111tewal (0 2ft]

·~
w.n.11X1....iar
2,/JsinZx •

s.!ed=
./3

a. {
tr 5tt lltt 17•}
frii·J2•1l
Dashboard SHS-GRl l -1S PREC-111 'Neel: 20 Second Quarter Exam Second Ouarler Exam
~ 34 Choose .tn expression for the apparem nth lfflll of the sequence AsSta'Tle that n begins with 1

·~
w.n.100....iar 1 + f. 1 +i,1 +;.1 +~.1 +¼,...

.. I l )"f11tl)

.. ,

I
d. a, ( · I)"• I

,. '
Choose.tnexpression for theapparefllnthtermofthesequence ASSl.methat nt)eon$wilh 1

1,-1, 1,-1,1, ....

C0nvefllhepolarequabonlorecbr91t1r form.

s- ~

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C0nvefllhepolarequ abonlo rectangu1.tr form.

,-~
,__
a. X1 •f • 2y • O
b. X'+y1 • 16

c• ./lx+y • O
d . X1 t f - 4y•0

Expand the bloomal by using Pasca's Triangle to oetemine the coefficients

~ ->tf

,.,,.._

I
a. 32x5 + 1ox'y + 40x~1 + 80x1'r + ~ + 16y5
b. ~ + 10x-v + 40xY + 80x1'r +,4Qxyl + 16Y5
c. ~ • 1ox4-y • 40xY • sox'-1 • soxv' • l2r
d. 2Jt5+ 20x'y+BOry! +80xf°r• 40xy'+32y5

~ ,. Oelefmine al soMloos of eac:tl equallol 1n raOlains (for x) or degrees (for 6) lo the nearesl lefllfl as appropnate

4 cos 2 :r - 1 • O

,.,,.._
a..9 + 2nn, 2.3 + 2nn, 3.6 • inn, 5.8 + 2nn, wtlefe n is any integer

b. i + 2n'lf,¥ + 2nn:.~ + ZM.~ + 2nll' w ht>rt n ts lln.y inttgt>r

c. i+ 2M,¥ + 11',!f- + 2m, ~ + 2rurwhfft n is any inttgff
Dashboard SHS-GRll-1S PREC-111
_,.
'Neel: 20 Second Quarter Exam Second Ouarler Exam

D e ~ .JI sdutions of eadl equaboi 111 radian$ (for x) or de!,ees (for 6) lo the ne.Yesl lenlh as appropriate

--
4 cos 2 x

b.
- 1• O

a . .9 + 2nn , 2.3 + 2nn, 3.6 + 2nn, 5.8 + 2nn, whefe n is any integer

i + 2rur. ~ + 2""•~ + ZM.~ + Z"" whtrt n ts a."y integ t r

c. i+ 2M,~ + lf,7 + 2nz.~ + Znx w htrt n is a..ny integtr
d. i + 2nll', 1l + 2mJ, ~ + 2nll', wit.er, n Is any ln.tlglT
c.1 + 11, 2.3 + 2nn, 3.3 - 2nn, 5.8 + 2nn , where n is any integer

o-- 39 Use the Blnomal Theorem to expand .n:I sin-., the expfflSSIOfl

--
(><' •,'f

a . -,.' +6H+ 41"y'+ 4x2),C + y'

b.3x1 + 2x'yZ + 9x'y'+ 4xly4 + 2/
c.r + 4H+sM+4x2v' + v'
d.x'+6,:Y + 4,:¥ +6xly'+ y'

UselheBn:lrnalTheoremtoe,rp,and.n:l~lheexpfe,.sion

--
(2x+ •f f

a .8x3+8x1y+4,cy2+2y
b. 8x3 + 12x2y + 6,cf + y3
c. 4x3+6xl y + 8,cf + y3
d.4x3 +6,cf +nx2y +y3

== j) [0] ■ m , ._• ..2 w ') CJ ... • ~ ? A 'Q ~)• GJ I~~~

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Howto v.tualLibr..y PoslstudcnlConccm CYRELJUUANP1U W
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QUIZ NAVIGATION

CYRELJUUAN PIU

~~~-.l~~~
-.
- •1
..,
Coovef1 Ile polar equabon lo recta~ar form.
r • 4csc:8

Sood-
a . X2 +4y - 4 • 0

~~;;;;~ b.jx1+,/'f • 6x2y - 2'y

c. 4x2 - Sf - 36y - 36 • 0

;;;;;;; d.y z 4

e . X2 • f - x213 • 0

i;;;;;;
;;;;;~;
;;;;;; ◄ Previous page

Show al QUeSboos on one page

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QUIZ NAVIGATION
Statef"nshed
C~letedon friday, 3November2017, 1249PM
CYREL JULIAN PILI Timetaken 2hotn34mins
Grade 46.00 out of 50 00 (92%)

o.-- 1 'Mile the first live terms of lhe sequence Assume ttial n begins wrth 1
A,,=n(n - l )(n-2)

' 24

o.-- 2 findlhesum.

1::. 110
Show all quesbons on one page
Fnshreview Answer: 40

o.-- 3 Calc!Aale lhe binomial coefficient

(100118)

Answer: 4950

findthe leoglhoflhearconacifdeof radiusi"ltercepledbyacenlralangle0

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