Trigonometry Examples

$\sin (- x) = - \sin (x)$

Step 1

Simplify the left side.

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Step 1.1

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

$- \sin (x) = - \sin (x)$

Step 2

Move all terms containing $\sin (x)$ to the left side of the equation.

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Step 2.1

Add $\sin (x)$ to both sides of the equation.

$- \sin (x) + \sin (x) = 0$

Step 2.2

Add $- \sin (x)$ and $\sin (x)$ .

$0 = 0$

Step 3

Since $0 = 0$ , the equation will always be true for any value of $x$ .

All real numbers

Step 4

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$