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# True or False: The domain of trigonometric functions can be restricted to any one of their branch(not necessarily principal value) in order to obtain their inverse function.

$\begin{array}{1 1} True \\ False \end{array}$

Ans - True

By choosing the proper interval with the same span as that of its corresponding
principal interval we can fix the domain.
That is for example principal interval of $sin^{-1}x$ is $(-\frac{\pi}{2},\frac{\pi}{2})$.We can fix any of theintervals,$(\frac{\pi}{2},\frac{3\pi}{2})\:\:or\:(\frac{3\pi}{2},\frac{5\pi}{2})$........ as the range of $sin^{-1}x$

edited Mar 10, 2013

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