Trigonometric Functions of Negative Angle

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Theorem

Sine Function is Odd

$\map \sin {-z} = -\sin z$

That is, the sine function is odd.


Cosine Function is Even

$\map \cos {-z} = \cos z$

That is, the cosine function is even.


Tangent Function is Odd

$\map \tan {-x} = -\tan x$

That is, the tangent function is odd.


Cotangent Function is Odd

$\map \cot {-x} = -\cot x$

That is, the cotangent function is odd.


Secant Function is Even

$\sec \left({-x}\right) = \sec x$

That is, the secant function is even.


Cosecant Function is Odd

$\csc \left({-x}\right) = -\csc x$

That is, the cosecant function is odd.


Sources