Inverse Trigonometric Functions Question 124
Question: If $ \frac{\pi }{2}\le x\le \frac{3\pi }{2}, $ then $ {{\sin }^{-1}}(\sin x) $ is equal to
Options:
A) $ x $
B) $ -x $
C) $ \pi +x $
D) $ \pi -x $
Show Answer
Answer:
Correct Answer: D
Solution:
We have $ \frac{\pi }{2}\le x\le \frac{3\pi }{2} $
$ \Rightarrow \frac{-\pi }{2}\le x-\pi \le \frac{\pi }{2}\Rightarrow \frac{-\pi }{2}\le \pi -x\le \frac{\pi }{2} $
$ \Rightarrow {{\sin }^{-1}}{\sin (\pi -x)}=\pi -x $ .
BETA
