Trigonometry Examples

$3 y = \tan (6 x)$

Step 1

Rewrite the equation as $\tan (6 x) = 3 y$ .

$\tan (6 x) = 3 y$

Step 2

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

$6 x = \arctan (3 y)$

Step 3

Divide each term in $6 x = \arctan (3 y)$ by $6$ and simplify.

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Step 3.1

Divide each term in $6 x = \arctan (3 y)$ by $6$ .

$\frac{6 x}{6} = \frac{\arctan (3 y)}{6}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $6$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{\arctan (3 y)}{6}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{\arctan (3 y)}{6}$