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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)

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) = ___. 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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