Precalculus
Exact Trig Values & Graphs Test REVIEW
Name ___________________________________Hour _______
Find the EXACT VALUE of each expression. Simplified radical form when necessary.
1. sin
2. csc
3. cos−1
4. cot
5. tan−1 −√3
6. cos−1
7. cot 5
8. tan−1(−1)
9. cos
10. tan
11. sin−1
13. tan cos−1
14. sec
degrees or radians
√
12. sec tan−1
√
15. sin cos−1
State the amplitude and period for each equation.
16.
= −3 sin
Amplitude = __________
17.
Period = __________
=
cos 4
Amplitude = __________
Period = __________
Write a sine equation with the following:
Write a cosine equation with the following:
18. Amp = 4
Period = 8
19. Amp = 6.5
Period =
Equation: _____________________________
Equation: _____________________________
Explain the difference in the graphs of the following equations. Be very specific!
20.
21.
1st:
= sin − 2 _________________
1st:
= 2 sin
2nd:
= sin( − 2) _________________
2nd:
= −2 sin
_____________________
_____________________
State the amplitude, period, phase shift (Be specific . . . left or right), and vertical shift (Be specific . . . up or down .
= sin
22.
+
23.
−4
amp:_______ period:_______ phase:________ vertical:________
= −3 cos ( − 3) + 1
24.
= 3 sin 2
−
+2
amp:______ period:______ phase:_______ vertical:________
25.
= cos
+
−5
amp:_______ period:_______ phase:________ vertical:________
amp:_______ period:______ phase:________vertical:_______
Write a sine equation with the following:
Write a cosine equation with the following:
26. Amp = 2
27. Amp = 2.5
Period =
Phase Shift = right
Phase Shift = left
Vertical Shift = 3 down
Equation: _____________________________
28.
Cos Equation:
___________________________________
Sin Equation:

3


3

3

3
2
3

4
3
29.
Cos Equation:
___________________________________
Sin Equation:
___________________________________
Vertical Shift = 2 up
Equation: _____________________________
Write a sine AND a cosine equation for the following graphs.
___________________________________
4
2

Period = 5
GRAPH the following equations. Label all tick marks appropriately and show more than one cycle.
30.
= −2 sin 2
32.
= tan
−
+1
State the period: ______
34.
= sec
State the period: ______
31.
= 5 cos ( + ) − 3
33.
= cot
State the period: ______
35.
= csc
State the period: ______