**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.