# Examples With Trigonometric Functions: Even, Odd Or Neither

In these lessons, we will look at how to determine whether a Trigonometric Function is 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

#### Examples With Trigonometric Functions: Even, Odd Or Neither

Example 2

Determine whether the following trigonometric function is Even, Odd or Neither
a) f(x) = sec x tan x

Example 3

b) g(x) = x4 sin x cos2x

Example 4

c) h(x) = cos x + sin x

#### How To Use The Even-Odd Properties Of The Trigonometric Functions?

Example: Find the exact value using even-odd properties.
(a) sin(-30°)
(b) cos(-3π/4)
(c) tan(-π/4)

#### How To Determine Trig Function Values Based Upon Whether The Function Is Odd Or Even?

Determine each function value.
If cos(x) = 0.5, then cos(-x) = ___.
If sin(x) = 0.15, then sin(-x) = ___.
If tan(-x) = -3, then tan(x) = ___.
If sec(-x) = 1.4, then sec(x) = ___.

#### How To Use Even Or Odd Properties To Evaluate Trig Functions?

Evaluate the trigonometric function by first using even/odd properties to rewrite the expression with a positive angle. Give an exact answer Do not use a calculator.
sin(-45°)
sec(210°)
cos(-π6)
csc(-3π/2)

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