Find the Reference Angle -(29pi)/9

$- \frac{29 π}{9}$

Step 1

Find an angle that is positive, less than $2 π$ , and coterminal with $- \frac{29 π}{9}$ .

Add $2 π$ to $- \frac{29 π}{9}$ .

$- \frac{29 π}{9} + 2 π$

The resulting angle of $- \frac{11 π}{9}$ is coterminal with $- \frac{29 π}{9}$ but isn\'t positive. Repeat the step.

$- \frac{11 π}{9}$

Add $2 π$ to $- \frac{11 π}{9}$ .

$- \frac{11 π}{9} + 2 π$

The resulting angle of $\frac{7 π}{9}$ is positive and coterminal with $- \frac{29 π}{9}$ .

$\frac{7 π}{9}$

Step 2

Since the angle $\frac{7 π}{9}$ is in the second quadrant, subtract $\frac{7 π}{9}$ from $π$ .

$π - \frac{7 π}{9}$

Step 3

Simplify the result.

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

$π \cdot \frac{9}{9} - \frac{7 π}{9}$

Combine fractions.

Combine $π$ and $\frac{9}{9}$ .

$\frac{π \cdot 9}{9} - \frac{7 π}{9}$

Combine the numerators over the common denominator.

$\frac{π \cdot 9 - 7 π}{9}$

Simplify the numerator.

Move $9$ to the left of $π$ .

$\frac{9 \cdot π - 7 π}{9}$

Subtract $7 π$ from $9 π$ .

$\frac{2 π}{9}$