Trigonometric Functions: Even, Odd Or Neither

What Is An Even Function?

An even function is symmetric (by reflection) about the y-axis , i.e.
f(-x) = f(x)

What Is An Odd Function?

An odd function is symmetric (by 180° rotation) about the origin, i.e.
f(-x) = -f(x)

The following table shows the Even Trigonometric Functions and Odd Trigonometric Functions. Scroll down the page for more examples and step by step solutions.

Even Trigonometric Functions And Identities

Cosine function is even. cos(-x) = cos x
Secant function is even. sec(-x) = sec x

Odd Trigonometric Functions And Identities

Sine function is odd. sin(-x) = – sin x
Cosecant function is odd. csc(-x) = – csc x
Tangent function is odd. tan(-x) = – tan x
Cotangent function is odd. cot(-x) = – cot x

Determine Whether A Trigonometric Function Is Odd, Even, Or Neither

Examples with Trigonometric Functions: Even, Odd or Neither
Cosine function, Secant function, Sine function, Cosecant function, Tangent function, and Cotangent function