Trigonometry Examples

$g (x) = \cot (x)$

Step 1

Find $f (- x)$ .

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Step 1.1

Find $g (- x)$ by substituting $- x$ for all occurrence of $x$ in $g (x)$ .

$g (- x) = \cot (- x)$

Step 1.2

Since $\cot (- x)$ is an odd function, rewrite $\cot (- x)$ as $- \cot (x)$ .

$g (- x) = - \cot (x)$

Step 2

A function is even if $f (- x) = f (x)$ .

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Step 2.1

Check if $f (- x) = f (x)$ .

Step 2.2

Since $- \cot (x)$ $\neq$ $\cot (x)$ , the function is not even.

The function is not even

Step 3

A function is odd if $f (- x) = - f (x)$ .

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Step 3.1

Multiply $- 1$ by $\cot (x)$ .

$- f (x) = - \cot (x)$

Step 3.2

Since $- \cot (x) = - \cot (x)$ , the function is odd.

The function is odd

Step 4