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Inverse Trigonometry Formula Sheet 1
Formula Sheet 1
Inverse Trigonometry Formula Sheet 2
Formula Sheet 2

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Summary:

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

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

\( \sin^{-1}x \) 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.