1
Algebra 3 Assignment Sheet
WELCOME TO TRIGONOMETRY, ENJOY YOUR STAY
(1) Assignment # 1 Complete the circle diagram
(2) Assignment # 2 Sine & Cosine functions chart
(3) Assignment # 3 Other Trig functions chart
(4) Assignment # 4 Finding other trig functions
(5) Assignment # 5 Review Worksheet
(6) TEST
(7) Assignment # 6 Angle Addition Formulas
(8) Assignment # 7 Double, Half-Angle Formulas
(9) Assignment # 8 Review Worksheet
(10) TEST
(11) Assignment # 9 Trig Identities (1)
(11) Assignment # 9 Trig Identities (2)
(12) Assignment # 10 Problems ( 1 9 ) Solving Trig Equations
(13) Assignment # 10 Problems ( 10 18 ) Solving Trig Equations
(14) Assignment # 11 Review Worksheet Solving Trig Equations
(15) TEST
INTRODUCTION TO TRIGONOMETRY
I Definition of radian: Radians are an angular measurement. One
radian is the measure of a central angle of a circle that is subtended by an
10
arc whose length is equal
to the radius of the circle.
x radius R
R5
Therefore:
arc length = angle in radians
3
2
The radius wraps itself around the circle 2 times. Approx. 6.28 times.
Therefore 360o = 2 R
1
2 R
R
o
1
Dividing you get 1
..
360o
180o
180o
R
Conversely ... 1 R
Ex. Change 60o to radians.
0 R2,
Change
R
to degrees.
4
3
Convert the2following from degrees to radians or vice versa:
1.
2.
3. 195
36o
320o
4.
15
5.
17
20
6.
5
3
II UNIT CIRCLE:
The unit circle is the circle with radius = 1, center is located at the origin.
What is the equation of this circle?
Important Terms:
A. Initial side:
B. Terminal side:
C. Coterminal angles:
D. Reference angles:
The initial and terminal sides form an angle at the center
if the terminal side rotates CCW, the angle is positive
if the terminal side rotates CW, the angle is negative
unit circle
coterminal
positive
negative
Coterminal angles have the same terminal side. -45 and 315 or
7
3
and
3
The reference angle is the acute angle made between the Terminal Side
and the x-axis
III GEOMETRY REVIEW
30 60 90
RIGHT TRIANGLES
45 45 - 90
45
60
2a
a
45
30
a 3
Therefore, for the Unit Circle, hypotenuse is always 1.
45
60
2/2
1/2
30
45
3/2
2/2
Algebra 3 Assignment # 1
Trigonometric Functions
Let theta represent the measure of the reference angle.
Three basic functions are sine, cosine and tangent.
They are written as sin , cos , and tan
Right triangle trigonometry -
SOHCAHTOA
sin
opp
hyp
cos
adj
hyp
tan
opp
adj
hyp
opp
adj
A. Find cos
B. Find sin
5 2
12
5
13
5 3
5
C. Find tan
D. Find sin
25
Triangles in the Unit Circle
B (0,1)
On the Unit Circle:
P(x,y)
sin
1
y
O
cos
A (1,0)
tan
Where functions are positive
II Reference Triangles
A. Drop from point to x-axis.
10
B. Examples
3
1. Find sin
4
coterminal angles
2. Find cos
4
3
Same as cos
4
R
coterminal angles
3. Find sin 420
coterminal angles
4. Find cos
6
13
5. Find sin =
cos =
11
12
III Quadrangle Angles
Def: An angle that has its terminal side on one of the coordinate axes.
To find these angles , use the chart
y
y
1
x
cos x
1
y
sin
tan
x cos
B (0,1)
sin
C (-1,0)
A (1,0)
D (0,-1)
Find the sine, cosine for all the quadrangles.
0 0 R
90
R
2
sin 0
cos 0
sin
cos
180 R
sin
cos
3
270 R
2
sin
cos
360 2 R
sin
cos
Trig values
13
Algebra 3 Assignment # 2
Complete each of the following tables please.
Radian
Measure
11
3
Degree
Measure
5
4
330o
19
6
450o
3
45o
210o
Sin
Cos
Radian
Measure
Degree
Measure
Sin
Cos
3
2
180o
7
3
4
150o
11
4
780o
90o
14
Answers
Radian
Measure
11
3
11
6
5
4
5
2
19
6
Degree
Measure
660o
330o
225o
450o
570o
45o
540o
210o
1
2
Sin
Cos
Radian
Measure
3
2
1
2
3
2
1
2
3
2
Degree
Measure
270o
Sin
Cos
2
2
2
7
3
180o 420o
3
2
1
2
1
0
1
2
3
2
2
2
2
2
7
6
3
2
5
6
13
3
11
4
150o
45o
780o
495o
90o
1
2
2
2
2
2
3
2
1
2
2
2
2
3
2
1
0
15
6.2 Other Trigonometric Functions
Sin
Cosecant:
Cos
Secant:
Tan
Cotangent:
http://mathplotter.lawrenceville.org/mathplotter/mathPage/trig.htm
Find the following values
1. csc
2. cot
5. tan
4
3
6. cot
4
3. sec2
4. sec
3
2
7. csc 3
8. tan
17
6
16
6.2 Algebra 3 Assignment # 3
Complete the following tables.
Radian
Measure
Degree
Measure
3
4
8
3
330
135
450
240
Sin
Cos
Tan
Cot
Sec
Csc
Radian
Measure
Degree
Measure
Sin
Cos
Tan
Cot
Sec
Csc
3
2
540
7
3
13
4
150
7
4
210
270
Alg 3(11)
Ch 6 Trig
17
Answers
Radian
Measure
Degree
Measure
8
3
11
6
3
4
480
330
135
450
30
2
2
1
2
2
2
3
2
2
2
3
2
Sin
1
2
1
2
3
2
5
2
2
2
3
4
135
4
3
900
240
3
2
1
2
Cos
Tan
1
3
Undef.
1
3
Cot
1
3
Undef.
1
3
Undef.
2
3
Undef.
7
3
5
6
13
4
7
6
7
4
3
2
420
150
585
315
270
Sec
2
3
Csc
2
3
3
2
Radian
Measure
Degree
Measure
270
540
Sin
Cos
Tan
Undef.
Cot
Undef.
Sec
Undef.
Csc
Undef.
1
2
3
2
1
3
1
3
2
3
1
2
3
2
2
3
2
2
2
2
210
1
2
2
2
2
3
3
2
2
2
1
3
Undef.
2
3
Undef.
1
Alg 3(11)
Ch 6 Trig
18
6.2 MORE TRIG FUNCTIONS
Identifying in which quadrant the angle lies
is
essential for having the correct signs of the
trig functions.
If given, Sin =
3
and if told that 0 , can we find the cos ?
2
5
1. Find cos if sin = 2/3 and 0 2
2. Find tan if sin = 3/7 and
Alg 3(11)
Ch 6 Trig
19
Alg 3(11)
Ch 6 Trig
20
3. Find csc if cos =
3
2
2
5. If Tan = -
3
3
and 2
2
, 270<360
5
4. Find sec if sin = -1/3 and
, find all the remaining functions of .
6. Find the values of the six trig. functions of , if is an angle in standard
position with the
point (-5, -12) on its terminal ray.
Alg 3(11)
Ch 6 Trig
21
Algebra 3 Assignment # 4
(1) Sin( ) =
3
,
5
(2) Cos( ) =
0 < < . Find the remaining 5 trig. functions of .
2
4
,
5 2
< < 3 . Find the remaining 5 trig. functions of .
2
(3) Tan( ) =
12
,
5
(4) Sec( ) =
7 3
,
2
5
(5) Csc( ) =
< < . Find the remaining 5 trig. functions of .
7
,
3
< < 2 . Find the remaining 5 trig. functions of .
180o < < 270o. Find the remaining 5 trig. functions of .
(6) Cot( ) = 2 , 270o < < 360o. Find the remaining 5 trig. functions of .
(7) Sin( ) =
24
,
25
180o < < 270o. Find the remaining 5 trig. functions of .
(8) Find the values of the six trig. functions of , if is an angle in standard position with the point (4 , 3) on
its terminal ray
(9) Find the values of the six trig. functions of , if is an angle in standard position with the point (5 , 12) on
its terminal ray
Trig Assignment #4 Answers
Alg 3(11)
Ch 6 Trig
(1) cos( ) =
(2) sin( ) =
22
4
5
3
5
, tan( ) =
3
4
, cot( ) =
4
3
, sec( ) =
2 6
7
, cos( ) =
(5) sin( ) = 73 , cos( ) =
(6) sin( ) =
, csc( ) =
5
3
3
5
, tan( ) = 4
, cot( ) = 4
3 , sec( ) = 4 , csc( ) =
5 , cot( ) =
(3) sin( ) = 12
13 , cos( ) =
13
(4) sin( ) =
5
4
5
7
, tan( ) =
2 10
7
1
, cos( ) =
5
5
12
2 6
5
, tan( ) =
13
, sec( ) = 13
5 , csc( ) =
12
, cot( ) =
3
, cot( ) =
2 10
2
, tan( ) =
5
, sec( ) =
5
2 6
2 10
3
5
2
, csc( ) =
, sec( ) =
24
7
3
(8) sin( ) = cos( ) =
5
3
, tan( ) = , cot( ) = 4 , sec( ) =
4
3
4
5
7
2 6
7
2 10
, csc( ) = 5
7
(7) cos( ) = 25
, tan( ) =
, cot( ) =
7
24
1
2
5
3
25
, sec( ) = 25
7 , csc( ) =
24
5
4
5
, csc( ) =
3
5
5
13
13
(9)sin( ) = 12 cos( ) =
, tan( ) = 12 , cot( ) =
, sec( ) =
, csc( ) =
13
13
5
12
5
12
Algebra 3 Review Worksheet
(1) Complete the following table please.
Alg 3(11)
Ch 6 Trig
Rad.
23
2
3
3
2
Deg.
10
3
135
150
330
9
4
750
240
sin
cos
tan
cot
sec
csc
(2) Sin(x) =
5
7
x
.
2
(3) Tan() =
1
2
0 90 .
(4) Cot(x) = 0.8 , x
(5) Sec() = 3 ,
3
2
Find the remaining 5 trig functions of x.
Find the remaining 5 trig functions of .
. Find the remaining 5 trig functions of x.
90 180 .
Find the remaining 5 trig functions of .
(6) Find the values of the six trig. functions of , if is an angle in standard position with the
point (5 , 3) on its terminal ray.
Algebra 3 Review Answers
(1)
Rad.
2
3
3
4
3
2
11
6
5
6
10
3
25
6
9
4
4
3
Alg 3(11)
Ch 6 Trig
24
Deg.
120
135
270
330
540
sin
3
2
2
2
cos
2
2
Undef
Undef
2
3
Undef
tan
cot
1
3
sec
csc
2
3
(2) cos(x) =
2 6
(3) sin() =
(4) sin(x) =
1
5
3
2
2
5
, cos(x) =
41
2 2
3
, cos() =
(6) sin() =
3
34
, cos() =
3
2
405
240
3
2
2
2
2
2
1
3
1
3
2
2
1
3
Undef
1
3
2
3
2
3
2
3
7
2 6
, csc(x) =
7
5
, cot(x) =
2 6
5
, tan(x) =
, tan() =
5
4
2 2
3
5
, sec(x) =
5
2
, csc() =
, sec(x) =
41
4
, cot() =
1
2 2
, cot() =
45
3
2
, tan() =
5
34
750
, cot() = 2 , sec() =
(5) sin() =
600
1
3
5
2 6
, tan(x) =
, cos() =
5
41
150
5,
3
2
3
2
2
41
5
, csc(x) =
, csc() =
3
2 2
sec() =
3
2
34
5
, csc() =
34
3
Alg 3(11)
Ch 6 Trig
25
ADDITION AND SUBTRACTION FORMULAS
sin
sin
cos
cos
+ = sin cos + cos sin
- = sin cos - cos sin
+ = cos cos - sin sin
- = cos cos + sin sin
tan + =
tan tan
1 tan tan
tan - =
tan tan
1 tan tan
30
SPECIAL ANGLES
2nd
3rd
4th
120
___
___
135
___
___
150
___
___
180
___
___
45
60o
90o
COMBINATIONS
15 =
345 =
255 =
5
=
12
0 R2,
3
2
Alg 3(11)
Ch 6 Trig
26
EXAMPLES
Evaluate each expression
1) sin 75
sin (45 + 30)
2) cos 345
3) tan
11
12
sin(120 45)
Alg 3(11)
Ch 6 Trig
27
Simplify the following:
4) cos (270 - x)
5) sin ( x +
)=
2
6) cos ( x + )
Alg 3(11)
Ch 6 Trig
28
Find each of the following numbers:
If sin A =
12
,0<A <
13
2
7) sin (A + B)
8) cos (A B)
9)
tan (A + B )
and
cos B =
8
3
, B
17
2
Alg 3(11)
Ch 6 Trig
29
Algebra 3 Trig Formulas Assignment #6
(1) Find each of the following numbers please.
(a) sin(15 )
(c) sin(105 )
13
12
(b) cos(15 )
(d) cos(75 )
11
12
(e) sin
(f) cos
(g) sin(345 )
(h) tan(15 )
(2) Simplify each of the following please.
(a) sin(90 + x)
(b) cos( x)
2
(c) sin(180 x)
(d) cos( + x)
(3) Sin(A) =
4
5
5
, A is in Quadrant I, Cos(B) = 13 , B is in Quadrant II.
Find each of the following numbers please.
(a) sin(A + B)
(b) cos(A + B)
(c) sin(A B)
(d) cos(A B)
(e) tan(A + B)
(f) csc(A B)
Alg 3(11)
Ch 6 Trig
30
Assignment #6
Answers
(1) (a)
6
4
(b)
6
4
(c)
6
4
(d)
6
4
(e)
2
4
(f)
(g)
2
4
(h) 2
(2) (a) cos x
(a)
6
4
(b) sin x
(c) sin x
(3)
(d) cos x
16
65
(b)
(c)
56
65
(d)
33
65
(e)
16
63
(f)
65
56
63
65
Alg 3(11)
Ch 6 Trig
31
DOUBLE AND HALF ANGLE FORMULAS
Double Angle Formulas
Half Angle Formulas
sin 2 = 2sincos
cos
cos 2 = cos2 - sin2
1 - 2sin2
1 cos
2
2
1 cos
sin
2
2
= 2cos 1
2
Find each of the following numbers, please.
1
2
1) sin ( 22 )
2) cos (
7
)
8
Alg 3(11)
Ch 6 Trig
32
If Sin A =
5
,
13
3
2
Find the following numbers, please.
3) sin (
4)
1
A)
2
cos (2B)
5) sin (A + B)
3
4
Tan B = ,
B
2
Alg 3(11)
Ch 6 Trig
33
Algebra 3 Double and Half Angle Formulas Assignment #7
(1) Find each of the following numbers please.
(a) sin(67 12
(b) cos
8
(d) cos(202 12
(c) sin
(2) Sin(A) =
4
5
, 2 < A < , Tan(B) =
12
5
, 32 < B < 2 . Find each of the
following numbers please.
(a) sin( 12 A)
(b) cos( 12 A)
(c) sin( 12 B)
(d) sec( 12 B)
(e) sin(2B)
(f) cos(2A)
(g) csc(A B)
(h) cos(A + B)
Alg 3(11)
Ch 6 Trig
34
Answers
(1) (a)
2
2
(b)
(c)
2
2
(d)
(2)
(a)
2
2
2
5
2
13
(d)
(e)
120
(f)
(g)
65
16
(h)
169
2
2
(b)
(c)
13
3
25
33
65
1
5
Alg 3(11)
Ch 6 Trig
35
Algebra 3 Formula Review Worksheet, Assignment #8
(1) Find each of the following numbers please.
(a) sin(15 )
(b) cos(105 )
(c) sin(195 )
(e) sin(112 12
(d) cos(285 )
7
(f) cos
12
(g) tan(75)
(h) sec
(2) Simplify each of the following please.
(b) cos( + x)
2
(a) sin(180 + x)
(c) sin(
3
x)
2
4
(3) Sin(A) = 5 , < A < 32 , Sec(B) =
(d) cos(180 x)
13
5
, 0 < B < 2 . Find each of the
following numbers.
(a) sin(A + B)
(b) cos(A + B)
(c) sin(A B)
(d) cos(A B)
(e) sin(2B)
A
(g) sin
(f) cos(2A)
A
(h) cos
Alg 3(11)
Ch 6 Trig
36
Answers
(1) (a)
6
4
2
2
or
(c)
2
4
(e)
2
2
(f)
(h)
(g)
or
2
2
2
2
or
(b) sin x
(c) cos x
(a)
6
4
(d)
(2) (a) sin x
(3)
2
4
(b)
(d) cos x
56
(b)
65
(c)
16
65
(d)
(e)
120
169
(f)
(g)
2
5
63
65
(h)
25
1
5
33
65
or
2
2
2
2
3
