HPC Inverse Trig Functions Practice
I. What is the range of values of arcsin (x) ?_________
What is the range of values of arccos (x) ?_________
What is the range of values of arctan (x) ?_________
II. Compute an exact value without using a calculator.
⎛ 1⎞
1. arcsin ⎜ − ⎟
⎝ 2⎠
⎛ 3⎞
2. sin −1 ⎜
⎜ 2 ⎟⎟
⎝
⎠
⎛
2⎞
3. arcsin ⎜ −
⎜ 2 ⎟⎟
⎝
⎠
⎛
2⎞
4. arccos ⎜ −
⎟
⎝ 2 ⎠
5. arccos(−1)
⎛
3⎞
6. arccos ⎜ −
⎜ 2 ⎟⎟
⎝
⎠
⎛ ⎛ π ⎞⎞
7. arctan ⎜ sin ⎜ ⎟ ⎟
⎝ ⎝ 2⎠⎠
⎛
3⎞
8. arctan ⎜ −
⎜ 3 ⎟⎟
⎝
⎠
9. arcsin sin ( 3)
1 ⎞
⎛
10. tan ⎜ arctan
⎟
3⎠
⎝
⎛
⎛ 12 ⎞ ⎞
13. cos ⎜ arctan ⎜ − ⎟ ⎟
⎝ 5 ⎠⎠
⎝
15.
⎛
⎛ 13 ⎞ ⎞
tan 2 ⎜ arcsec ⎜ − ⎟ ⎟
⎝ 12 ⎠ ⎠
⎝
(
⎛ 13π ⎞
11. arcsin ⎜ sin
12 ⎟⎠
⎝
)
4⎞
⎛
12. cos ⎜ arcsin ⎟
5⎠
⎝
14. sin ( arccos ( 2x ))
( )
⎛
⎛ 1⎞ ⎞
16. sin ⎜ arctan − 3 − arcsin ⎜ − ⎟ ⎟
⎝ 2⎠ ⎠
⎝