Find the Reference Angle (34pi)/3

$\frac{34 π}{3}$

Step 1

Find an angle that is positive, less than $2 π$ , and coterminal with $\frac{34 π}{3}$ .

Subtract $2 π$ from $\frac{34 π}{3}$ .

$\frac{34 π}{3} - 2 π$

The resulting angle of $\frac{28 π}{3}$ is positive, less than $2 π$ , and coterminal with $\frac{34 π}{3}$ .

$\frac{28 π}{3}$

Subtract $2 π$ from $\frac{28 π}{3}$ .

$\frac{28 π}{3} - 2 π$

The resulting angle of $\frac{22 π}{3}$ is positive, less than $2 π$ , and coterminal with $\frac{34 π}{3}$ .

$\frac{22 π}{3}$

Subtract $2 π$ from $\frac{22 π}{3}$ .

$\frac{22 π}{3} - 2 π$

The resulting angle of $\frac{16 π}{3}$ is positive, less than $2 π$ , and coterminal with $\frac{34 π}{3}$ .

$\frac{16 π}{3}$

Subtract $2 π$ from $\frac{16 π}{3}$ .

$\frac{16 π}{3} - 2 π$

The resulting angle of $\frac{10 π}{3}$ is positive, less than $2 π$ , and coterminal with $\frac{34 π}{3}$ .

$\frac{10 π}{3}$

Subtract $2 π$ from $\frac{10 π}{3}$ .

$\frac{10 π}{3} - 2 π$

The resulting angle of $\frac{4 π}{3}$ is positive, less than $2 π$ , and coterminal with $\frac{34 π}{3}$ .

$\frac{4 π}{3}$

Step 2

Since the angle $π$ is in the third quadrant, subtract $π$ from $\frac{4 π}{3}$ .

$\frac{4 π}{3} - π$

Step 3

Simplify the result.

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

$\frac{4 π}{3} - π \cdot \frac{3}{3}$

Combine fractions.

Combine $- π$ and $\frac{3}{3}$ .

$\frac{4 π}{3} + \frac{- π \cdot 3}{3}$

Combine the numerators over the common denominator.

$\frac{4 π - π \cdot 3}{3}$

Simplify the numerator.

Multiply $3$ by $- 1$ .

$\frac{4 π - 3 π}{3}$

Subtract $3 π$ from $4 π$ .

$\frac{π}{3}$