Find the Reference Angle -pi/5

$- \frac{π}{5}$

Step 1

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

Add $2 π$ to $- \frac{π}{5}$ .

$- \frac{π}{5} + 2 π$

The resulting angle of $\frac{9 π}{5}$ is positive and coterminal with $- \frac{π}{5}$ .

$\frac{9 π}{5}$

Step 2

Since the angle $\frac{9 π}{5}$ is in the fourth quadrant, subtract $\frac{9 π}{5}$ from $2 π$ .

$2 π - \frac{9 π}{5}$

Step 3

Simplify the result.

To write $2 π$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$2 π \cdot \frac{5}{5} - \frac{9 π}{5}$

Combine fractions.

Combine $2 π$ and $\frac{5}{5}$ .

$\frac{2 π \cdot 5}{5} - \frac{9 π}{5}$

Combine the numerators over the common denominator.

$\frac{2 π \cdot 5 - 9 π}{5}$

Simplify the numerator.

Multiply $5$ by $2$ .

$\frac{10 π - 9 π}{5}$

Subtract $9 π$ from $10 π$ .

$\frac{π}{5}$