Find the Reference Angle -(19pi)/4

$- \frac{19 π}{4}$

Step 1

Find an angle that is positive, less than $2 π$ , and coterminal with $- \frac{19 π}{4}$ .

Add $2 π$ to $- \frac{19 π}{4}$ .

$- \frac{19 π}{4} + 2 π$

The resulting angle of $- \frac{11 π}{4}$ is coterminal with $- \frac{19 π}{4}$ but isn\'t positive. Repeat the step.

$- \frac{11 π}{4}$

Add $2 π$ to $- \frac{11 π}{4}$ .

$- \frac{11 π}{4} + 2 π$

The resulting angle of $- \frac{3 π}{4}$ is coterminal with $- \frac{19 π}{4}$ but isn\'t positive. Repeat the step.

$- \frac{3 π}{4}$

Add $2 π$ to $- \frac{3 π}{4}$ .

$- \frac{3 π}{4} + 2 π$

The resulting angle of $\frac{5 π}{4}$ is positive and coterminal with $- \frac{19 π}{4}$ .

$\frac{5 π}{4}$

Step 2

Since the angle $π$ is in the third quadrant, subtract $π$ from $\frac{5 π}{4}$ .

$\frac{5 π}{4} - π$

Step 3

Simplify the result.

To write $- π$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{5 π}{4} - π \cdot \frac{4}{4}$

Combine fractions.

Combine $- π$ and $\frac{4}{4}$ .

$\frac{5 π}{4} + \frac{- π \cdot 4}{4}$

Combine the numerators over the common denominator.

$\frac{5 π - π \cdot 4}{4}$

Simplify the numerator.

Multiply $4$ by $- 1$ .

$\frac{5 π - 4 π}{4}$

Subtract $4 π$ from $5 π$ .

$\frac{π}{4}$