Download Trigonometry Review Problems

Trigonometry Review Problems
Pre-Calculus Chapter 5
Draw the angle, and name its quadrant. Find a positive and negative co-terminal angle. Convert.
1. -465°
8
2.
3
-465° = ______ radians
Quadrant:_____
Positive co-terminal angle:_____ ° = ______ rad.
Negative co-terminal angle_____ ° = ____ rad.
8
= ____ °
3
Quadrant:_____
Positive co-terminal angle:_____ ° = ______ rad.
Negative co-terminal angle_____ ° = ____ rad.
Find the reference angle for the given angle θ in standard position.
3. 295°
4. -490°
10
5.
3
θ′ = _________
θ′ = _________
θ′ = _________
6.
5
8
θ′ = _________
Use the ordered pairs from the unit circle to find the exact value of each expression.
7. cos 150°
8. sin 225°
9. tan (-30°)
10. csc(90°)
11. sec(270°) 12. cot 45°
13. sin

3
14. cos 52
15. cot 116
16. sec( 73 )
19. Determine each value to four decimal places.
8
b) sec( 130  )
 5
a) tan
c) cot   
5
 3
17. csc(5 )
18. tan 72
d) csc(340°)
Find values for θ where…
20. 0° < θ < 360° to the nearest tenth of a degree
21. 0 < θ < 2π to the nearest hundredth of a radian
sin θ = -0.3568
cot θ = 1.2479
θ = ___________________
θ = ___________________
In which quadrant does the terminal side of θ lie from standard position?
22. tan θ > 0 and csc θ < 0
23. sec θ < 0 and π < θ < 2π
24. cot    3 5 5 and sin  
70
14
Given the following information, find the exact value of the six trig functions.
25. (5, 9) is a point on the terminal side of θ.
26. The terminal side of θ intersects the unit circle
 2 5 5
.
,
at  

5
5


sin θ = ______ cos θ = ______ tan θ = ______
sin θ = ______ cos θ = ______ tan θ = ______
csc θ = ______ sec θ = ______ cot θ = ______
7 2
and cos θ > 0 (Draw the Δ.)
2
csc θ = ______ sec θ = ______ cot θ = ______
19
28.  
6
sin θ = ______ cos θ = ______ tan θ = ______
sin θ = ______ cos θ = ______ tan θ = ______
csc θ = ______ sec θ = ______ cot θ = ______
csc θ = ______ sec θ = ______ cot θ = ______
27. csc   
Graph at least two cycles of the following functions.
30. g ( x)  3 csc( 2x)
29. f ( x)  tan 14 x
Period:_______
Domain:____________________________
Range: _____________________________
31. h( x)  2 cot(3x   )
Period:_______
Domain:____________________________
Range: _____________________________
32. j ( x)   cos( 12 x   )  3
Period:________ Phase Shift:_________
Domain:____________________________
Range: _____________________________
Period:____ Phase Shift:____ Vert. Trans:_____
Domain:____________________________
Range: _____________________________