Find the Reference Angle (23pi)/8

$\frac{23 π}{8}$

Step 1

Find an angle that is positive, less than $2 π$ , and coterminal with $\frac{23 π}{8}$ .

Subtract $2 π$ from $\frac{23 π}{8}$ .

$\frac{23 π}{8} - 2 π$

The resulting angle of $\frac{7 π}{8}$ is positive, less than $2 π$ , and coterminal with $\frac{23 π}{8}$ .

$\frac{7 π}{8}$

Step 2

Since the angle $\frac{7 π}{8}$ is in the second quadrant, subtract $\frac{7 π}{8}$ from $π$ .

$π - \frac{7 π}{8}$

Step 3

Simplify the result.

To write $π$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$π \cdot \frac{8}{8} - \frac{7 π}{8}$

Combine fractions.

Combine $π$ and $\frac{8}{8}$ .

$\frac{π \cdot 8}{8} - \frac{7 π}{8}$

Combine the numerators over the common denominator.

$\frac{π \cdot 8 - 7 π}{8}$

Simplify the numerator.

Move $8$ to the left of $π$ .

$\frac{8 \cdot π - 7 π}{8}$

Subtract $7 π$ from $8 π$ .

$\frac{π}{8}$