Curcular Definition of Trigonometric Functions
Trigonometric functions are first defined for acute (less than the right) angles such that may be encountered in right triangles. If abc and a'b'c' are two similar right triangles, then, say,
where sin (reads sine) and cos (reads cosine) are the most fundamental trigonometric functions. In addition we have
and there are more.
As can be seen, the functions are defined not just for acute angles. The above definitions are extended to make sine and cosine periodic with period 2π:
The extensions are made according to the following rules:
As a consequence, tangent and cotangent aquire a period of π:
Sine is set to be odd:
Cosine is even:
This make tangent and cotangent odd.
Versine is defined as
This function is used only rarely. However we did stumble on an example where it proved useful.
Secant and cosecant are the reciprocals of cosine and sine, respectively:
The derivatives of sine and cosine are among the first obtained in calculus:
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