Find the Reference Angle (-7pi)/3

$\frac{- 7 π}{3}$

Step 1

Find an angle that is positive, less than $2 π$ , and coterminal with $\frac{- 7 π}{3}$ .

Add $2 π$ to $\frac{- 7 π}{3}$ .

$\frac{- 7 π}{3} + 2 π$

The resulting angle of $- \frac{π}{3}$ is coterminal with $\frac{- 7 π}{3}$ but isn\'t positive. Repeat the step.

$- \frac{π}{3}$

Add $2 π$ to $- \frac{π}{3}$ .

$- \frac{π}{3} + 2 π$

The resulting angle of $\frac{5 π}{3}$ is positive and coterminal with $\frac{- 7 π}{3}$ .

$\frac{5 π}{3}$

Step 2

Since the angle $\frac{5 π}{3}$ is in the fourth quadrant, subtract $\frac{5 π}{3}$ from $2 π$ .

$2 π - \frac{5 π}{3}$

Step 3

Simplify the result.

To write $2 π$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$2 π \cdot \frac{3}{3} - \frac{5 π}{3}$

Combine fractions.

Combine $2 π$ and $\frac{3}{3}$ .

$\frac{2 π \cdot 3}{3} - \frac{5 π}{3}$

Combine the numerators over the common denominator.

$\frac{2 π \cdot 3 - 5 π}{3}$

Simplify the numerator.

Multiply $3$ by $2$ .

$\frac{6 π - 5 π}{3}$

Subtract $5 π$ from $6 π$ .

$\frac{π}{3}$