Name_______________________________ Per:_____ Date:_________
13.1 and 13.2 Review
For questions 1-2, find the reference angle.
1. 220
2. 175
For questions 3-6, find a coterminal angle between 0 and 360 .
3. −310
4. 764
5. 625
6. −405
For questions 7-10, convert each degree measure into radians or each radian measure into degrees.
π
16π
7. −72
8.
9. 210
10. −
3
9
11. Fill out the unit circle with the coordinates, degrees, and radians.
For questions 12-20, find the exact value for each trigonometric value. (Hint: Use your unit circle.)
12. cos 210 =
13. sin − π =
14. cos − 45 =
15. sin
5π
=
4
16. sin 30 =
18. cos
5π
=
6
19. cos
4π
=
3
17. sin135 =
20. tan
π
3
=
For questions 21-28, find all possible angles 0 ≤ θ ≤ 360 and 0 ≤ θ ≤ 2π that makes the statement true.
21. cos θ =
3
2
23. sin θ = −
22. cos θ = 1
3
2
24. sin θ =
2
2
25. 6cos θ = −3
26. −2 = −2 + cos θ
27. −6 cos θ = 3 2
28. 4sin θ = 2 3
For questions 29-31, graph the function in both degrees and radians. Then fill out the characteristics.
29. y = sin x
Domain:
Range:
Domain:
Range:
Period:
Amplitude:
Period:
Amplitude:
Zeros:
y-intercept:
Zeros:
y-intercept:
Midline/Sinusoidal Axis:
Midline/Sinusoidal Axis:
Minimums (x-coordinates):
Maximums (x-coordinates):
30. y = cos x
Domain:
Range:
Domain:
Range:
Period:
Amplitude:
Period:
Amplitude:
Zeros:
y-intercept:
Zeros:
y-intercept:
Midline/Sinusoidal Axis:
Midline/Sinusoidal Axis:
Minimums (x-coordinates):
Maximums (x-coordinates):
Name_______________________________ Per:_____ Date:_________
31. y = tan x
Domain:
Range:
Domain:
Range:
Period:
y-intercept:
Period:
y-intercept:
Zeros:
Zeros:
Asymptotes:
Asymptotes:
For questions 32-43, tell whether each statement that describes a characteristic of the sine function,
cosine function, or tangent function is true or false.
32. Sine models the horizontal position of an object moving around a unit circle.
33. Cosine increases throughout the interval 180 ≤ θ ≤ 360 .
34. The domain of tangent is all real angles.
35. The graph of cosine crosses the θ − axis at integer multiples of 180 .
36. The amplitude of tangent is 1.
37. Sine and cosine have a period of π .
38. Sine has positive function values in the interval 0 < θ < 180 .
39. Cosine has negative function values in the interval 90 < θ < 270 .
40. Tangent passes through ( 0, 0 ) .
41. Cosine is increasing on the interval 0 ≤ θ ≤
π
2
.
42. Tangent has a period of 2π .
43. Cosine has a sinusoidal axis (midline) of y = 0 .