Find the Reference Angle -(16pi)/7

$- \frac{16 π}{7}$

Step 1

Find an angle that is positive, less than $2 π$ , and coterminal with $- \frac{16 π}{7}$ .

Add $2 π$ to $- \frac{16 π}{7}$ .

$- \frac{16 π}{7} + 2 π$

The resulting angle of $- \frac{2 π}{7}$ is coterminal with $- \frac{16 π}{7}$ but isn\'t positive. Repeat the step.

$- \frac{2 π}{7}$

Add $2 π$ to $- \frac{2 π}{7}$ .

$- \frac{2 π}{7} + 2 π$

The resulting angle of $\frac{12 π}{7}$ is positive and coterminal with $- \frac{16 π}{7}$ .

$\frac{12 π}{7}$

Step 2

Since the angle $\frac{12 π}{7}$ is in the fourth quadrant, subtract $\frac{12 π}{7}$ from $2 π$ .

$2 π - \frac{12 π}{7}$

Step 3

Simplify the result.

To write $2 π$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$2 π \cdot \frac{7}{7} - \frac{12 π}{7}$

Combine fractions.

Combine $2 π$ and $\frac{7}{7}$ .

$\frac{2 π \cdot 7}{7} - \frac{12 π}{7}$

Combine the numerators over the common denominator.

$\frac{2 π \cdot 7 - 12 π}{7}$

Simplify the numerator.

Multiply $7$ by $2$ .

$\frac{14 π - 12 π}{7}$

Subtract $12 π$ from $14 π$ .

$\frac{2 π}{7}$