Find the Reference Angle (33pi)/10

$\frac{33 π}{10}$

Step 1

Find an angle that is positive, less than $2 π$ , and coterminal with $\frac{33 π}{10}$ .

Subtract $2 π$ from $\frac{33 π}{10}$ .

$\frac{33 π}{10} - 2 π$

The resulting angle of $\frac{13 π}{10}$ is positive, less than $2 π$ , and coterminal with $\frac{33 π}{10}$ .

$\frac{13 π}{10}$

Step 2

Since the angle $π$ is in the third quadrant, subtract $π$ from $\frac{13 π}{10}$ .

$\frac{13 π}{10} - π$

Step 3

Simplify the result.

To write $- π$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$\frac{13 π}{10} - π \cdot \frac{10}{10}$

Combine fractions.

Combine $- π$ and $\frac{10}{10}$ .

$\frac{13 π}{10} + \frac{- π \cdot 10}{10}$

Combine the numerators over the common denominator.

$\frac{13 π - π \cdot 10}{10}$

Simplify the numerator.

Multiply $10$ by $- 1$ .

$\frac{13 π - 10 π}{10}$

Subtract $10 π$ from $13 π$ .

$\frac{3 π}{10}$