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Examples with Trigonometric Functions: Even, Odd or Neither

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In this lesson we will look at how to determine whether a Trigonometric Function is Even, Odd or Neither.



 

What is an even function?
1. An even function is symmetric about the y-axis.
2. f(-x) = f(x)

What is an odd function?
1. An odd function is symmetric about the origin.
2. 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



Example 2
Determine whether the following trigonometric function is Even, Odd or Neither
a) f(x) = sec x tan x Examples with Trigonometric Functions: Even, Odd or Neither
Example 3
b) g(x) = x4 sin x cos2x Examples with Trigonometric Functions: Even, Odd or Neither
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)


Trigonometry Calculator with step by step solutions
Right Triangle Trigonometry, Radian Measure and Circular Functions
Graphing Trigonometric Functions, Simplifying Trigonometric Expressions
Verifying Trigonometric Identities, Verifying Trigonometric Identities
Using Fundamental Identities, Solving Trigonometric Equations
Complex Numbers, Analytic Geometry in Polar Coordinates
Exponential and Logarithmic Functions, Vector Arithmetic, Vectors

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