page_title: Inverse trigonometric functions
section_title: Relationships among the inverse trigonometric functions
hierarchical_section_title: Inverse trigonometric functions / Basic properties / Relationships among the inverse trigonometric functions
context_page_description: In mathematics, the inverse trigonometric functions are the inverse functions of the trigonometric functions. Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions, and are used to obtain an angle from any of the angle's trigonometric ratios. Inverse trigonometric functions are widely used in engineering, navigation, physics, and geometry.
context_section_description: Complementary angles:
  Negative arguments:
  Reciprocal arguments:
  Useful identities if one only has a fragment of a sine table:
  Whenever the square root of a complex number is used here, we choose the root with the positive real part (or positive imaginary part if the square was negative real).
  A useful form that follows directly from the table above is
  .
  It is obtained by recognizing that .
  From the half-angle formula, , we get:
caption: The usual principal values of the arcsin(x) (red) and arccos(x) (blue) functions graphed on the cartesian plane.