Name______________________________________Period_______Date__________________
GSE PreCalculus
Section 4.4 Practice
SHOW ALL WORK WHERE NECESSARY!!!
The point is on the terminal side of an angle in standard position. Determine the exact
values of the six trigonometric functions of the angle.
1. (4, 3)
2. (-8, -15)
3. (12, -5)
4. (2, -4)
Find the values of the six trigonometric functions of Ɵ.
5. sin 𝜃 =
3
5
𝜃 𝑙𝑖𝑒𝑠 𝑖𝑛 𝑞𝑢𝑎𝑑 𝐼𝐼
Find the reference angle for the angle Ɵ.
7. 𝜃 = 120°
9. 𝜃 =
5𝜋
3
6. tan 𝜃 = −
sin 𝜃 < 0
8. 𝜃 = −135°
10. 𝜃 = −
5𝜋
6
15
8
Evaluate the sine, cosine and tangent of the angle without using a calculator.
12. −720°
11.225°
13. −495°
14. −
11𝜋
16. −
15.
4
3𝜋
4
10𝜋
3
Find the indicated trig value.
3
17.sin 𝜃 = − , 𝑖𝑛 𝑞𝑢𝑎𝑑 𝐼𝑉, cos 𝜃 = _______
5
5
18. cos 𝜃 = , 𝑖𝑛 𝑞𝑢𝑎𝑑 𝐼, sec 𝜃 = _______
8
5
19. tan 𝜃 = − , 𝑖𝑛 𝑞𝑢𝑎𝑑 𝐼𝑉, csc 𝜃 = _______ 20. csc 𝜃 = −2, 𝑖𝑛 𝑞𝑢𝑎𝑑 𝐼𝑉, cot 𝜃 = _______
4
Use a calculator to evaluate the trigonometric functions. Round your answer to four
decimal places.
2𝜋
22. tan 245°
21. tan
9
23. csc 320°
25. cos (−
15𝜋
14
24. sec 4.1
)
26. sin 10°
Find two solutions of the equation. Give you answers in degrees (𝟎° ≤ 𝜽 ≤ 𝟑𝟔𝟎°) and
radians (𝟎 ≤ 𝜽 ≤ 𝟐𝝅). No calculator.
1
28. csc 𝜃 = 2
27.sin 𝜃 =
2
29. cot 𝜃 = −√3
30. cos 𝜃 = 0