gives the cosine of z.


  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • The argument of Cos is assumed to be in radians. (Multiply by Degree to convert from degrees.) »
  • Cos is automatically evaluated when its argument is a simple rational multiple of ; for more complicated rational multiples, FunctionExpand can sometimes be used. »
  • For certain special arguments, Cos automatically evaluates to exact values.
  • Cos can be evaluated to arbitrary numerical precision.
  • Cos automatically threads over lists.


  • Cos is the cosine function, which is one of the basic functions encountered in trigonometry. It is defined for real numbers by letting be a radian angle measured counterclockwise from the axis along the circumference of the unit circle. Cos[x] then gives the horizontal coordinate of the arc endpoint. The equivalent schoolbook definition of the cosine of an angle in a right triangle is the ratio of the length of the leg adjacent to to the length of the hypotenuse.
  • Cos threads element-wise over lists and matrices. When given numbers as arguments, Cos may be evaluated to arbitrary numeric precision. MatrixFunction can be used to give the cosine of a square matrix (i.e. the power series for the cosine function with ordinary powers replaced by matrix powers) as opposed to the cosines of the individual matrix elements, which is common for solving systems of ordinary differential equations arising from Newton's equation of motion.
  • Cos automatically evaluates to exact values when its argument is a simple rational multiple of . For more complicated rational multiples, FunctionExpand can sometimes be used to obtain an explicit exact value. Other operations useful for manipulation of symbolic expressions involving Cos include TrigToExp, TrigExpand, Simplify, and FullSimplify.
  • Cos satisfies the identity , which is equivalent to the Pythagorean theorem. The definition of the cosine function is extended to complex arguments using the definition , where is the base of the natural logarithm. The cosine function is entire, meaning it is complex differentiable at all finite points of the complex plane.
  • The inverse function of Cos is ArcCos. The hyperbolic cosine is given by Cosh.
Introduced in 1988
| Updated in 1999