## Trigonometric functions

All trigonometric functions use radians when an angle is called for. The ratio of degrees to radians is 180°/n.

The standard trignometric functions. y = sin (x), y = cos (x), and y = tan (x). arcsin (x [, y]) arccos (x [, y]) arctan (x [, y])

The inverse trigonometric functions: y = sin-1 (x), y = cos-1 (x), y = tan-1 (x) . These return the value of y (in radians) such that sin (y) = x with y G f]; cos (y) = x with y £ [0,7r]; and tan (y) = x with y £ [—f, f], respectively.

Returns tan-1 (f^") but takes into account the sign on x\ and x2 to place the angle in the correct quadrant. The angle y is returned in the full range —n < y < tv. The angle is chosen so that sin (y) = , ^ ^, and cos (y) = —¡£2==. Particular values are showin in the following table:

 Xl x2 y = arctan2 (x'i, x2) 0 1 0 1 0 2 0 -1 7T -1 0 Returns y = \Jx\ + xr,. Given a complex number in cartesian form, arctan2 and hypot can be used to compute phase and magnitude, quickly. Computes y = sinh (x) which is defined as ^ (e1 — e~x). Computes y = cosh (x) which is defined as ^ (ex + e~x). tanh (x [, y]) Computes y = tanh (x) which is defined as (ex — e-x) / (ex + e-x). arcsinh (x [, y]) arccosh (x [, y]) arctanh (x [, y]) These compute the inverse hyperpolic functions. y = arcfunc (x) is the (principal) value of y such that func (y) = x.