Find the Reference Angle -(10pi)/3

$- \frac{10 π}{3}$

Step 1

Find an angle that is positive, less than $2 π$ , and coterminal with $- \frac{10 π}{3}$ .

Add $2 π$ to $- \frac{10 π}{3}$ .

$- \frac{10 π}{3} + 2 π$

The resulting angle of $- \frac{4 π}{3}$ is coterminal with $- \frac{10 π}{3}$ but isn\'t positive. Repeat the step.

$- \frac{4 π}{3}$

Add $2 π$ to $- \frac{4 π}{3}$ .

$- \frac{4 π}{3} + 2 π$

The resulting angle of $\frac{2 π}{3}$ is positive and coterminal with $- \frac{10 π}{3}$ .

$\frac{2 π}{3}$

Step 2

Since the angle $\frac{2 π}{3}$ is in the second quadrant, subtract $\frac{2 π}{3}$ from $π$ .

$π - \frac{2 π}{3}$

Step 3

Simplify the result.

To write $π$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$π \cdot \frac{3}{3} - \frac{2 π}{3}$

Combine fractions.

Combine $π$ and $\frac{3}{3}$ .

$\frac{π \cdot 3}{3} - \frac{2 π}{3}$

Combine the numerators over the common denominator.

$\frac{π \cdot 3 - 2 π}{3}$

Simplify the numerator.

Move $3$ to the left of $π$ .

$\frac{3 \cdot π - 2 π}{3}$

Subtract $2 π$ from $3 π$ .

$\frac{π}{3}$