Sin has series expansion about the origin. The sine function is entire, meaning it is complex differentiable at all finite points of the complex plane. The definition of the sine function is extended to complex arguments using the definition, where is the base of the natural logarithm. Sin satisfies the identity, which is equivalent to the Pythagorean theorem. Sin is periodic with period, as reported by FunctionPeriod.the power series for the sine function with ordinary powers replaced by matrix powers). In contrast, MatrixFunction can be used to give the sine of a square matrix (i.e. Sin threads element-wise over lists and matrices.Other operations useful for manipulation of symbolic expressions involving Sin include TrigToExp, TrigExpand, Simplify, and FullSimplify. When given exact numeric expressions as arguments, Sin may be evaluated to arbitrary numeric precision. To specify an argument using an angle measured in degrees, the symbol Degree can be used as a multiplier (e.g. For more complicated rational multiples, FunctionExpand can sometimes be used to obtain an explicit exact value. Sin automatically evaluates to exact values when its argument is a simple rational multiple of. The equivalent schoolbook definition of the sine of an angle in a right triangle is the ratio of the length of the leg opposite to the length of the hypotenuse. Sin then gives the vertical coordinate of the arc endpoint. It is defined for real numbers by letting be a radian angle measured counterclockwise from the axis along the circumference of the unit circle. Sin is the sine function, which is one of the basic functions encountered in trigonometry.
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