Trigonometry Examples

$θ = \frac{11 π}{6}$

Step 1

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

$\frac{y}{x} = \tan (\frac{11 π}{6})$

Step 2

Solve for $y$ .

Tap for more steps...

Step 2.1

Multiply both sides by $x$ .

$\frac{y}{x} x = \tan (\frac{11 π}{6}) x$

Step 2.2

Simplify.

Tap for more steps...

Step 2.2.1

Simplify the left side.

Tap for more steps...

Step 2.2.1.1

Cancel the common factor of $x$ .

Tap for more steps...

Step 2.2.1.1.1

Cancel the common factor.

$\frac{y}{x} x = \tan (\frac{11 π}{6}) x$

Step 2.2.1.1.2

Rewrite the expression.

$y = \tan (\frac{11 π}{6}) x$

Step 2.2.2

Simplify the right side.

Tap for more steps...

Step 2.2.2.1

Simplify $\tan (\frac{11 π}{6}) x$ .

Tap for more steps...

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 fourth 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 $\frac{\sqrt{3}}{3}$ .

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