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If $ \sin^{-1} x=y$ then:

\[ (A) \quad 0 \leq y \leq \pi \qquad (B) \quad -\frac {\pi} {2} \leq y \leq \frac{\pi}{2} \] \[ (C) \quad 0 < y < \pi \qquad (B) \quad -\frac{\pi}{2} < y < \frac{\pi}{2} \]
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1 Answer

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Toolbox:
  • The range of the principal value of $\sin^{-1}x$ is $\left [ -\large\frac{\pi}{2}, \large\frac{\pi}{2} \right ]$
Since the range of the principal value of $\sin^{-1}x$ is $\left [ -\large\frac{\pi}{2},\large \frac{\pi}{2} \right ]$, if $\sin^{-1}x =y$, then $y$ must be in the range of the principal value.
 
Therefore, $(B): -\large\frac{\pi}{2} \leq y \leq \large\frac{\pi}{2}$ is the correct answer.

 

answered Mar 2, 2013 by balaji.thirumalai
edited Mar 15, 2013 by thanvigandhi_1
 
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