TRIGONOMETRIC FUNCTIONS TEST

1. Given the sinusoidal function

f(x) = —3cos (-52 -=) —

err / }
a '/4, TT /
[7 iaite —TT7 bpere- aT
we TE j
7)

2tore
<r)
ST. i
rs=
“a >
é
=
Y
|
f ~

ns
~ 4 t 1/2

| V O -Y2 /2 oO. | Ya |
7 a. Prepare a transformed table of values for one rotation
b. Graph at least one rotation of the function and identify the amplitude,
period and axis
matt i. » — "y ir bey ‘
te J : ‘

y=
7
—

- e-Me, —_—t

/ SS = on

21, } tera?

/ ie
_
-) (
“Ti
N}a <n
“> }
pe = — 2
"y f f2 te
“TT
$i oe — 27
2°T 1 2,
—
_
= =
aT ~25S
“

/ = = '— 42

”) (™ g \ “ry ; ~/f Tt “—~ j tt 2 T —olj, —n |

= f “-y ‘wuss “2 — em = ~ comer : ie } ‘Ty .

a fi. } ‘S - 2. 4 P lo a

I Pym: ry | 4 TT/ “7 . CORY| a ;

-—fot) ry S
— ‘) = ie 4 / $ =~ / 3 2 <— f b Ls ew
om -_

|
=
(tj)
\
of }
2Q =
27 -W,_ {2
aD
=
-ot 1, . »
oa - me
97, 26
Ue

7 fur “tf - ou/ _ = | TI/ —ist/s \ &

~ -_—f= \ > = f Ss4 = (3 /3 a ~ OF_A _ fr © nd
iJ

‘ se . TT . _ )% wat

/2.) z Z ~'/2 bo :
_ ) f y L \ _ Te on bo { “T eT _ 21). = ~~ £O mee [

“Th . —_ e »
7
a \
|(stp\> | _Tz= = —loW, 1, 2 ~NTW Ja 5 = =22T//
/ 0
— L6D

me (2 +
‘\ a
Th L —_ =|
I a} “F a
T
h — ~
IPT + wm ff
2 715 amp 4
aA | j * — < — \
XY — »

PEW

oo _

\
\
\
&
\
\

~ :

SS \

tenes eon er

Loé ° L a
ls C10 A Fr t f
~ b f a)

December 9%, 2022 MHF4U

 TRIGONOMETRIC FUNCTIONS TEST
[39

2. Convert to radians. /2

192° —_ \%0
XK Tw

= 192°
lox
K=%.251032104 wd

3. Convert each radian measure to degrees. /4

a. 2.75 radians b. -=

X= 180 xX _ _ \¥0
lis ON -st Tr
, 59734 ra
Ve 159.5633957 | . 1)
Ms Lee =
2y &,)

4. Determine the exact value of the trigonometric ratio in proper form. /2

nano era qaatnan

111 | =
V3
NeZz
=.2 -\)3
/Z a. Ug
me
cot—6 = —-y,
tay it y get

/(0 _ 2.

“YS
> 1+.
VS ~ 3

5. Determine the possible angle measures in radians on the interval [0,27]. Round
answers to two decimal places. /4
a. cos@=—- b. tang ==
4 7

O= 26472 O= 0.%5

~Orr0t 13
6. Determine three equivalent trigonometric ratios for
310 ,
—— Tt (277 \
f = "\
nrc | ott \
COS (- =}
4 = Cos ( — ) = (CoS(s-) = (0 | 7]
u C4 / \ Ww
Q% Q4 Q2 (3

December 9%, 2022 MHF4U ps. 2

 TRIGONOMETRIC FUNCTIONS TEST
/39
7. The equation for the height, h(t), of a Ferris wheel car, in metres, above the ground after f
seconds of rotation is given by the equation:
/10
670
h(t) = —12.5cos = G) +14
27

a) If riders get on at the bottom of the Ferris wheel, how far off the ground is the
loading platform?

| . S ww

b) How long does it take the Ferris wheel to make one rotation?
p ZT o |
Taiod = “Gy— =2N x22 = —54 =
q SOcanr che
“2° 4 otr
f io j ow LOA

c) Determine the height the Ferris Wheel car after 15 seconds.

WSS = LO.2Sm

g) Determine the first two times that the cart is at a height of 20 metres

“O> - 42.5 «5 f Ty. \ yyy

, 24ytts prt 99 fU0C f
f (>
:
ot
ena
|].OSLOOTT
j 2“ Wi fy FU SY
Starag
cfs ah)

Co | —_—— \ ot
| —|2eS ] ~ qq C

f 2 eA =| f f lo \ Ps d,s, <> 2 eZ eee ali

C6s C12.5) = <«£.* 1 41 S505 Sece aat hy fp

/4

rst
BE ?

i |

BONUS: Determine a second equation for the above sinusoidal graph

(\ a / NN
+(x) =_ 2 Cos (IT (% —\.S ) } 4. 7

(x +O ‘S) :
December 9%, 2022 MHF4U ps. 3