Find the Reference Angle (41pi)/12

$\frac{41 π}{12}$

Step 1

Find an angle that is positive, less than $2 π$ , and coterminal with $\frac{41 π}{12}$ .

Subtract $2 π$ from $\frac{41 π}{12}$ .

$\frac{41 π}{12} - 2 π$

The resulting angle of $\frac{17 π}{12}$ is positive, less than $2 π$ , and coterminal with $\frac{41 π}{12}$ .

$\frac{17 π}{12}$

Step 2

Since the angle $π$ is in the third quadrant, subtract $π$ from $\frac{17 π}{12}$ .

$\frac{17 π}{12} - π$

Step 3

Simplify the result.

To write $- π$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$\frac{17 π}{12} - π \cdot \frac{12}{12}$

Combine fractions.

Combine $- π$ and $\frac{12}{12}$ .

$\frac{17 π}{12} + \frac{- π \cdot 12}{12}$

Combine the numerators over the common denominator.

$\frac{17 π - π \cdot 12}{12}$

Simplify the numerator.

Multiply $12$ by $- 1$ .

$\frac{17 π - 12 π}{12}$

Subtract $12 π$ from $17 π$ .

$\frac{5 π}{12}$