Find the Reference Angle -(4pi)/5

$- \frac{4 π}{5}$

Step 1

Find an angle that is positive, less than $2 π$ , and coterminal with $- \frac{4 π}{5}$ .

Add $2 π$ to $- \frac{4 π}{5}$ .

$- \frac{4 π}{5} + 2 π$

The resulting angle of $\frac{6 π}{5}$ is positive and coterminal with $- \frac{4 π}{5}$ .

$\frac{6 π}{5}$

Step 2

Since the angle $π$ is in the third quadrant, subtract $π$ from $\frac{6 π}{5}$ .

$\frac{6 π}{5} - π$

Step 3

Simplify the result.

To write $- π$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{6 π}{5} - π \cdot \frac{5}{5}$

Combine fractions.

Combine $- π$ and $\frac{5}{5}$ .

$\frac{6 π}{5} + \frac{- π \cdot 5}{5}$

Combine the numerators over the common denominator.

$\frac{6 π - π \cdot 5}{5}$

Simplify the numerator.

Multiply $5$ by $- 1$ .

$\frac{6 π - 5 π}{5}$

Subtract $5 π$ from $6 π$ .

$\frac{π}{5}$