Precalculus Examples

$θ = \frac{5 π}{6}$

Step 1

Apply the formula $\frac{y}{x} = \tan (θ)$ .

$\frac{y}{x} = \tan (\frac{5 π}{6})$

Step 2

Solve for $y$ .

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Step 2.1

Multiply both sides by $x$ .

$\frac{y}{x} x = \tan (\frac{5 π}{6}) x$

Step 2.2

Simplify.

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Step 2.2.1

Simplify the left side.

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Step 2.2.1.1

Cancel the common factor of $x$ .

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Step 2.2.1.1.1

Cancel the common factor.

$\frac{y}{x} x = \tan (\frac{5 π}{6}) x$

Step 2.2.1.1.2

Rewrite the expression.

$y = \tan (\frac{5 π}{6}) x$

Step 2.2.2

Simplify the right side.

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Step 2.2.2.1

Simplify $\tan (\frac{5 π}{6}) x$ .

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Step 2.2.2.1.1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because tangent is negative in the second quadrant.

$y = - \tan (\frac{π}{6}) x$

Step 2.2.2.1.2

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

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

Step 2.2.2.1.3

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

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