Trigonometry Examples

$\tan (\frac{π}{6}) = \frac{y}{x}$

Step 1

Solve for $y$ .

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Step 1.1

Rewrite the equation as $\frac{y}{x} = \tan (\frac{π}{6})$ .

$\frac{y}{x} = \tan (\frac{π}{6})$

Step 1.2

Multiply both sides by $x$ .

$\frac{y}{x} x = \tan (\frac{π}{6}) x$

Step 1.3

Simplify.

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Step 1.3.1

Simplify the left side.

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Step 1.3.1.1

Cancel the common factor of $x$ .

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Step 1.3.1.1.1

Cancel the common factor.

$\frac{y}{x} x = \tan (\frac{π}{6}) x$

Step 1.3.1.1.2

Rewrite the expression.

$y = \tan (\frac{π}{6}) x$

Step 1.3.2

Simplify the right side.

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Step 1.3.2.1

Simplify $\tan (\frac{π}{6}) x$ .

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Step 1.3.2.1.1

The exact value of $\tan (\frac{π}{6})$ is $\frac{\sqrt{3}}{3}$ .

$y = \frac{\sqrt{3}}{3} x$

Step 1.3.2.1.2

Combine $\frac{\sqrt{3}}{3}$ and $x$ .

$y = \frac{\sqrt{3} x}{3}$

Step 2

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.