Find the Reference Angle -pi/9

$- \frac{π}{9}$

Step 1

Find an angle that is positive, less than $2 π$ , and coterminal with $- \frac{π}{9}$ .

Add $2 π$ to $- \frac{π}{9}$ .

$- \frac{π}{9} + 2 π$

The resulting angle of $\frac{17 π}{9}$ is positive and coterminal with $- \frac{π}{9}$ .

$\frac{17 π}{9}$

Step 2

Since the angle $\frac{17 π}{9}$ is in the fourth quadrant, subtract $\frac{17 π}{9}$ from $2 π$ .

$2 π - \frac{17 π}{9}$

Step 3

Simplify the result.

To write $2 π$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$2 π \cdot \frac{9}{9} - \frac{17 π}{9}$

Combine fractions.

Combine $2 π$ and $\frac{9}{9}$ .

$\frac{2 π \cdot 9}{9} - \frac{17 π}{9}$

Combine the numerators over the common denominator.

$\frac{2 π \cdot 9 - 17 π}{9}$

Simplify the numerator.

Multiply $9$ by $2$ .

$\frac{18 π - 17 π}{9}$

Subtract $17 π$ from $18 π$ .

$\frac{π}{9}$