# 2. Inverse Trigonometric Functions

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# Inverse Trigonometric Functions Class 12 Maths

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Summary:

The ranges (principal value branches) of inverse trigonometric functions are given in the following table:

 Functions Range $\sin^{-1}x$ $\left[ \frac{-\pi}{2}, \frac{\pi}{2} \right]$ $\csc^{-1}x$ $\left[ \frac{-\pi}{2}, \frac{\pi}{2} \right] – {0}$ $\tan^{-1}x$ $\left( \frac{-\pi}{2}, \frac{\pi}{2} \right)$ $\cos^{-1}x$ $[0, \pi]$ $\sec^{-1}x$ $[0, \pi] – { \frac{\pi}{2} }$ $\cot^{-1}x$ $(0, \pi)$

$\sin^{-1}x$ should not be confused with $(\sin x)^{-1}$. In fact $(\sin x)^{-1} = \frac{1}{\sin x}$ and similarly for other trigonometric functions.

The value of an inverse trigonometric functions which lies in its principal value branch is called the principal value of that inverse trigonometric functions.

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