Question

If $ \theta ={{\sin }^{-1}}[\sin (-600{}^\circ )], $ then one of the possible values of $ \theta $ is:

• A. $ \frac{\pi }{3} $
• B. $ \frac{\pi }{2} $
• C. $ \frac{2\pi }{3} $
• D. $ -\frac{2\pi }{3} $
• E. 0

Answer 1

Answer: (A)

$ \theta ={{\sin }^{-1}}\{-\sin 600{}^\circ \}={{\sin }^{-1}}\{-\sin 240{}^\circ \} $ $ ={{\sin }^{-1}}\left( \frac{\sqrt{3}}{2} \right) $ $ \Rightarrow $ $ \theta =60{}^\circ =\frac{\pi }{3} $