Download Lesson 4-3 Practice

4-3 Trig on the Unit Circle
NAME:__________________________
ASSIGNMENT
DATE:_______
Find the RATIO of the trig function indicated. Do NOT find the actual measure of the angle!
1.
2.
3.
4.
Use the given point on the terminal side of the angle 𝜃 to find the trigonometric function indicated.
5.
6.
Draw the reference triangle. Find the EXACT value of the trig ratio for 𝜽.
7. cot 𝜃 for �−√19, −9�
8. tan 𝜃 for �−2√3, −2�
Draw the reference triangle. Find the EXACT value of the trig ratio for 𝜽.
17
9
3𝜋
9. Given sec 𝜃 = − 15 and sin 𝜃 is positive.
10. Given csc 𝜃 = − 7 where 2 < 𝜃 < 2𝜋.
Find tan 𝜃.
Find tan 𝜃.
Find the reference angle.
11. 200°
12. 340°
13. 104°
14. −136°
Find the exact value WITHOUT USING THE UNIT CIRCLE AND TABLE!
15. sin 240°
16. cos(−225)°
17. tan 315°
18. csc(−90)°
Find the exact value WITHOUT USING THE UNIT CIRCLE AND TABLE!
𝜋
7𝜋
3𝜋
20. tan(− 6 )
21. sin 4
19. cos 4
22. cot(−
3𝜋
4
)
If 𝟎° ≤ 𝜽 ≤ 𝟑𝟑𝟑°, then find 𝜽 WITHOUT USING THE UNIT CIRCLE AND TABLE!
√3
√2
26. sec 𝜃 = −2
25. tan 𝜃 = −√3
23. sin 𝜃 =
24. cos 𝜃 = −
2
2
27. Find all six trig functions. Fill in the table. WITHOUT USING THE UNIT CIRCLE AND TABLE!
radians
𝟕𝟕
𝟒
𝐬𝐬𝐬 𝜽
𝐜𝐜𝐜 𝜽
𝐭𝐭𝐭 𝜽
Use the table to find the EXACT value USING THE UNIT CIRCLE AND TABLE!
11𝜋
3𝜋
28. csc 120°
29. sin
30. cot �− �
6
2
𝐜𝐜𝐜 𝜽
𝐬𝐬𝐬 𝜽
31. cot(−90°)
Use the table to find the angle where 𝟎° ≤ 𝜽 ≤ 𝟑𝟑𝟑° USING THE UNIT CIRCLE AND TABLE!
2√3
√2
34. cot 𝜃 = undefined
35. sec 𝜃 = 2
32. cos 𝜃 = −
33. csc 𝜃 =
2
3
Use the calculator to find the APPROXIMATE value of each. Round to the nearest hundredth.
36. csc 70°
37. cot −120°
38. sec 150°
39. sin 66°
𝐜𝐜𝐜 𝜽
Use the calculator to find each angle where 𝟎° ≤ 𝜽 ≤ 𝟑𝟑𝟑°. Round to the nearest hundredth.
40. sin 𝜃 = 0.95105
41. sec 𝜃 = −1.36
42. cos 𝜃 = 0.46
APPLICATION
Fill in every angle measure in degrees, radians, and give the coordinates of the point on the unit circle.
Fill in the missing parts of the table.
degrees
radians
π
3
𝐬𝐬𝐬 𝜽
3
2
𝐜𝐜𝐜 𝜽
−
𝐭𝐭𝐭 𝜽
𝐜𝐜𝐜 𝜽
𝐬𝐬𝐬 𝜽
𝐜𝐜𝐜 𝜽
- degree
1
2
−120°
−1
- radian
ANSWERS TO UNIT 9 CORRECTIVE ASSIGNMENT!
5
2.
1. 3
√19
9
17
3.
8
√3
3
7.
13. 76°
√2
19. − 2
25. 120°, 300°
√3
20. − 3
26. 120°, 240°
radians
21.
27.
31. 0
25
7√2
8
√2
−2
−
√2
2
𝐜𝐜𝐜 𝜽
√2
2
sin θ
cos θ
3
120°
2π
3
3
2
−1
2
240°
4π
3
2
−1
2
0
-1
−
3
tan θ
𝐭𝐭𝐭 𝜽
𝐜𝐜𝐜 𝜽
−1
−√2
32. 135°, 225°
3
− 3
3
0
csc θ
5. 2
11. 20°
6. − 2
23. 60°, 120°
24. 135°, 225°
12. 20°
17. −1
16.
22. 1
𝐬𝐬𝐬 𝜽
3
√5
37. 0.58
38. −1.15
42. 62.61°, 297.39°
π
π
4√21
10. −
√3
2
√2
2
radians
𝟕𝟕
𝟒
1
2
180°
8
15. −
3
2
60°
4.
9. − 15
8.
14. 44°
1
30. 0
29. − 2
36. 1.06
35. 60°, 300°
41. 137.33°, 222.67°
degrees
√2
4
sec θ
𝐬𝐬𝐬 𝜽
√2
𝐜𝐜𝐜 𝜽
−1
33. 60°, 120°
39. 0.91
cot θ
- degree
18. −1
28.
2√3
3
34. 0°/360°, 180°
40. 72°, 108°
- radian
2
3
3
-300°
−
5π
3
2 3
3
-2
− 3
3
-240°
−
4π
3
−2 3
3
-2
3
3
-120°
Und
-1
Und
-180°
2 3
3
−
2π
3
−π