6.3E: Inverse Trigonometric Functions (Exercises)
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- Jan 2, 2021
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Section 6.3 Exercises
Evaluate the following expressions, giving the answer in radians.
1. sin−1(√22)
2. sin−1(√32)
3. sin−1(−12)
4. sin−1(−√22)
5. cos−1(12)
6. cos−1(√22)
7. cos−1(−√22)
8. cos−1(−√32)
9. tan−1(1)
10. tan−1(√3)
11. tan−1(−√3)
12. tan−1(−1)
Use your calculator to evaluate each expression, giving the answer in radians.
13. cos−1(−0.4)
14. cos−1(0.8)
15. sin−1(−0.8)
16. tan−1(6)
Find the angle θ in degrees.
17. 
18.
Evaluate the following expressions.
19. sin−1(cos(π4))
20. cos−1(sin(π6))
21. sin−1(cos(4π3))
22. cos−1(sin(5π4))
23. cos(sin−1(37))
24. sin(cos−1(49))
25. cos(tan−1(4))
26. tan(sin−1(13))
Find a simplified expression for each of the following.
27. sin(cos−1(x5)), for −5≤x≤5
28. tan(cos−1(x2)), for −2≤x≤2
29. sin(tan−1(3x))
30. cos(tan−1(4x))
- Answer
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1. π4
3. −π6
5. π3
7. 3π4
9. π4
11. −π3
13. 1.9823
15. -0.9273
17. 44.427∘
19. π4
21. −π6
23. 2√107
25. 1√17
27. √25−x25
29. 3x√9x2+1
