8 Review

Key
Name____________________

Date____________________

#1-9. Find the exact value of the trigonometric function. (no calc)
5𝜋 5𝜋 5𝜋 5𝜋
1. cos ( 6 ) 2. 𝑠𝑖𝑛 ( 6 ) 3. 𝑡𝑎𝑛 ( 6 ) 4. 𝑠𝑒𝑐 ( 6 )

k Ya By 373 231
5. cot(3𝜋) 6. csc(3𝜋) 7. csc(−225°) 8. sec(−225°)

und und Fa Fa
𝜋 𝜋
9. sin⁡2 ( 2 ) + ⁡ cos⁡2 ( 2 )⁡
L
#10-11. Prove the equations are identities
FEE
ItCUFO CSCO
tarotkseco
10.
1+𝑡𝑎𝑛𝜃
=
𝑠𝑒𝑐 2 𝜃+2𝑡𝑎𝑛𝜃
11. ⁡(𝑡𝑎𝑛𝜃)(1 − 𝑐𝑜𝑡 2 𝜃) + (𝑐𝑜𝑡𝜃)(1 − 𝑡𝑎𝑛2 𝜃) = 0

Iot IÉÉ
tana tancutzo cute cotttank
1−𝑡𝑎𝑛𝜃 2−𝑠𝑒𝑐 2 𝜃

hno EEI.EE twto EEosIEo

tan cotta tant
ff
ity.fi D
II c tÉEM
#12-13. Use a calculator to solve for 𝑥, 0 ≤ 𝑥 ≤ 2𝜋

12. csc 𝑥⁡ < 0.3 13. cos 𝑥 = 0.65

y isoxDx 865.42A19g
y U for 6.28
 A
14. A signal buoy bobs up and down so that at time t (in seconds) it is sin 𝑡 feet
above the average water level. A bell rings whenever the buoy is 3 inches above
the average water level. What are the time intervals between bell rings as the
water rises and falls? Answer accurate to two decimal places.
FSM X
t 8
2513inch

i
y

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15. Consider the function 𝑦 = 3𝑠𝑖𝑛(2𝑥) + 𝑐𝑜𝑠(2𝑥 + 1)

4 35naxltcos.CZ xtYz
2.85 25 20
6.5 2 85 3.650
a) Use a graphing calculator to find the phase shift of this sinusoid.

b) Use a graphing calculator to find an equivalent function in the form

b
2Eo12A
𝑦 = 𝐴𝑠𝑖𝑛(𝑏𝑥 + 𝑐)

2.23S1hC2xt 24 2.2 Y 0 24
16. State the period, domain, range and amplitude of:
1
a) 𝑦 = 3𝑠𝑖𝑛 2 𝑥 − 5 b) 𝑦 = 7 sin(𝜋𝑥) + 11

per 2 2 41 Per 25 2
dom C as as dom aid
Range 8 2 71198114,18
AMP
17. Find 3 2
cos 𝜃 if sin 𝜃 = − 3 and tan 𝜃 > 0. (no calc)
S A
226232
cost.rs

It 47,3

12
CUSO
18. Solve sec 𝜃 = −2 for 0 ≤ 𝜃 ≤ 360° (no calc)

Yz
0 120042400
180

20
#19-25. Sketch the graph of one complete cycle of the given equation and find
the necessary information.

19. 𝑦 = 2 sin(2𝑥)

2
Amplitude_____ Period____ MET
cas a
Domain________ Nitzstyi
E 2,2
Range_________

20. 𝑦 = −3 cos(𝜋𝑥) − 1

3 Hit 2
Amplitude_____ Period____

Cas as
Domain________
7
E 4,2
Range_________

1 4
p
21. 𝑦 = 2 sec 𝑥

2T
Period____
2asx
It I
342 21T
Allrealexcept
Domain________ 2,372,1542 42
I
C 236,03
I
Range_________
as

22. 𝑦 = tan⁡(0.5𝑥) n
21T I 1
21T
Period____

IMI o 1
Allrealexcept IT Ist Ist
Domain________

Cas as
Range_________

n i
 Ift y
23. 𝑦 = 3 csc(2𝑥) I
4 381124
TI
Period____ 242 1
all real
Domain________ except d I
II
C d 3713,0 972,4
Range_________ I I1
24. 𝑦 = tan(3𝜋𝑥) + 1 l ta in
1
113
Period____ HIT 3 I
upl
all real s except
Domain________

C o.o
Range_________
146,1
25. 𝑦 = −2𝑐𝑜𝑡𝑥 tgi 1
IT
Period____

all real except

Domain________ d it
O IT I2t I 1
d o
Range_________

#26-27. Determine whether the equation for the graph has the form 𝑦 = 𝐴𝑠𝑖𝑛𝐵𝑥
or 𝑦 = 𝐴𝑐𝑜𝑠𝐵𝑥 ( with 𝐵 > 0 ) and then find the values of A and B.

per 8T
26. 27.
per L
W

2I 8I
Form:_______________
YACOSBX YASINBX
Form:_______________

4 44
A:________B:_________ 2 IT
A:________B:_________
#28-29. Write an equation for the given graph.

SM 2 1
6

28.
GEE 29.

tantax
Equation:_________________ oscax
Equation:__________________ I

30. Refer to the graph of 𝑦 = − sin 𝑥 in the figure. Specify the coordinates of the
point F.

31T O
IT31T

𝑐𝑜𝑠2 𝑥+⁡𝑠𝑖𝑛2 𝑥

Tsin
31. Use the Pythagorean identities to simplify: 𝑐𝑜𝑡 2 +1

1 𝜋
32. In the expression √𝑢2 +7
⁡let 𝑢 = √7 tan 𝜃, where 0 ≤ 𝜃 ≤ and simplify the
2
result.

Fang t tap g

Fo
r
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