Find the Reference Angle -(42pi)/8

$- \frac{42 π}{8}$

Step 1

Find an angle that is positive, less than $2 π$ , and coterminal with $- \frac{42 π}{8}$ .

Add $2 π$ to $- \frac{42 π}{8}$ .

$- \frac{42 π}{8} + 2 π$

The resulting angle of $- \frac{13 π}{4}$ is coterminal with $- \frac{42 π}{8}$ but isn\'t positive. Repeat the step.

$- \frac{13 π}{4}$

Add $2 π$ to $- \frac{13 π}{4}$ .

$- \frac{13 π}{4} + 2 π$

The resulting angle of $- \frac{5 π}{4}$ is coterminal with $- \frac{42 π}{8}$ but isn\'t positive. Repeat the step.

$- \frac{5 π}{4}$

Add $2 π$ to $- \frac{5 π}{4}$ .

$- \frac{5 π}{4} + 2 π$

The resulting angle of $\frac{3 π}{4}$ is positive and coterminal with $- \frac{42 π}{8}$ .

$\frac{3 π}{4}$

Step 2

Since the angle $\frac{3 π}{4}$ is in the second quadrant, subtract $\frac{3 π}{4}$ from $π$ .

$π - \frac{3 π}{4}$

Step 3

Simplify the result.

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

$π \cdot \frac{4}{4} - \frac{3 π}{4}$

Combine fractions.

Combine $π$ and $\frac{4}{4}$ .

$\frac{π \cdot 4}{4} - \frac{3 π}{4}$

Combine the numerators over the common denominator.

$\frac{π \cdot 4 - 3 π}{4}$

Simplify the numerator.

Move $4$ to the left of $π$ .

$\frac{4 \cdot π - 3 π}{4}$

Subtract $3 π$ from $4 π$ .

$\frac{π}{4}$