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.

Share this page to Google Classroom

Related Pages
Lessons On Trigonometry
Inverse trigonometry
Trigonometric Functions
Even And Odd Functions

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.

Trigonometric Even Odd Functions

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.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
Mathway Calculator Widget

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.