Trigonometry Examples

$y = \tan (b x)$

Step 1

Rewrite the equation as $\tan (b x) = y$ .

$\tan (b x) = y$

Step 2

Take the inverse tangent of both sides of the equation to extract $x$ from inside the tangent.

$b x = \arctan (y)$

Step 3

Divide each term in $b x = \arctan (y)$ by $b$ and simplify.

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Step 3.1

Divide each term in $b x = \arctan (y)$ by $b$ .

$\frac{b x}{b} = \frac{\arctan (y)}{b}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $b$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{b x}{b} = \frac{\arctan (y)}{b}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{\arctan (y)}{b}$