Trigonometric functions ----------------------- Except where otherwise noted, the trigonometric functions take a radian angle as input and the inverse trigonometric functions return radian angles. The ordinary trigonometric functions are single-valued functions defined everywhere in the complex plane (except at the poles of tan, sec, csc, and cot). They are defined generally via the exponential function, e.g. .. math :: \cos(x) = \frac{e^{ix} + e^{-ix}}{2}. The inverse trigonometric functions are multivalued, thus requiring branch cuts, and are generally real-valued only on a part of the real line. Definitions and branch cuts are given in the documentation of each function. The branch cut conventions used by mpmath are essentially the same as those found in most standard mathematical software, such as Mathematica and Python's own cmath libary (as of Python 2.6; earlier Python versions implement some functions erroneously). Degree-radian conversion ........................................................... :func:degrees ^^^^^^^^^^^^^^^^ .. autofunction:: mpmath.degrees(x) :func:radians ^^^^^^^^^^^^^^^^ .. autofunction:: mpmath.radians(x) Trigonometric functions ....................... :func:cos ^^^^^^^^^^^^^^^^ .. autofunction:: mpmath.cos(x, **kwargs) :func:sin ^^^^^^^^^^^^^^^^ .. autofunction:: mpmath.sin(x, **kwargs) :func:tan ^^^^^^^^^^^^^^^^ .. autofunction:: mpmath.tan(x, **kwargs) :func:sec ^^^^^^^^^^^^^^^^ .. autofunction:: mpmath.sec(x) :func:csc ^^^^^^^^^^^^^^^^ .. autofunction:: mpmath.csc(x) :func:cot ^^^^^^^^^^^^^^^^ .. autofunction:: mpmath.cot(x) Trigonometric functions with modified argument ........................................................ :func:cospi ^^^^^^^^^^^^^^^^ .. autofunction:: mpmath.cospi(x, **kwargs) :func:sinpi ^^^^^^^^^^^^^^^^ .. autofunction:: mpmath.sinpi(x, **kwargs) Inverse trigonometric functions ................................................ :func:acos ^^^^^^^^^^^^^^^^ .. autofunction:: mpmath.acos(x, **kwargs) :func:asin ^^^^^^^^^^^^^^^^ .. autofunction:: mpmath.asin(x, **kwargs) :func:atan ^^^^^^^^^^^^^^^^ .. autofunction:: mpmath.atan(x, **kwargs) :func:atan2 ^^^^^^^^^^^^^ .. autofunction:: mpmath.atan2(y, x) :func:asec ^^^^^^^^^^^^^^^^ .. autofunction:: mpmath.asec(x) :func:acsc ^^^^^^^^^^^^^^^^ .. autofunction:: mpmath.acsc(x) :func:acot ^^^^^^^^^^^^^^^^ .. autofunction:: mpmath.acot(x) Sinc function ............. :func:sinc ^^^^^^^^^^^^^^^^ .. autofunction:: mpmath.sinc(x) :func:sincpi ^^^^^^^^^^^^^^^^ .. autofunction:: mpmath.sincpi(x)