Inverse Trigonometric functions

  • Inverse trigonometric functions are used to find the angle that corresponds to a given value of a trigonometric function.
  • The inverse trigonometric functions are denoted by arcsin, arccos, arctan, arccsc, arcsec, and arccot.
  • The domain and range of the inverse trigonometric functions depend on the choice of branch, which is determined by the sign of the argument.
  • The inverse trigonometric functions are commonly used to solve trigonometric equations and to find the angles of right triangles given their sides.
  • The inverse trigonometric functions can also be used to convert between rectangular and polar coordinates.

Important Formulas to Remember in these Inverse Trigonometric functions

  • \( \sin^{-1}x+y=\sin^{-1}(x\sqrt{1-y^2}+y\sqrt{1-x^2}) \)
  • \( \cos^{-1}x+y=\cos^{-1}(x\sqrt{1-y^2}-y\sqrt{1-x^2}) \)
  • \( \tan^{-1}x+y=\tan^{-1}(\frac{x+y}{1-xy}) \)