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More Lessons for Trigonometry

Math Worksheets

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)

**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) = x^{4} sin x cos^{2}x
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) = ___.**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)

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More Lessons for Trigonometry

Math Worksheets

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

1. An even function is symmetric about the y-axis.

2. f(-x) = f(x)

1. An odd function is symmetric about the origin.

2. f(-x) = -f(x)

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

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

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

Examples with Trigonometric Functions: Even, Odd or Neither

Cosine function, Secant function, Sine function, Cosecant function, Tangent function, and Cotangent function

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) = x

Example 4

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

Example: Find the exact value using even-odd properties.

(a) sin(-30°)

(b) cos(-3π/4)

(c) tan(-π/4)

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) = ___.

sin(-45°)

sec(210°)

cos(-π6)

csc(-3π/2)

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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