Trigonometric Functions of Negative Angle

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

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

That is, the secant function is even.

Cosecant Function is Odd

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

That is, the cosecant function is odd.

Sources

• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions: Functions of Angles in All Quadrants in terms of those in Quadrant I