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 $- \frac{41 π}{12}$ .

Add $2 π$ to $- \frac{41 π}{12}$ .

$- \frac{41 π}{12} + 2 π$

The resulting angle of $- \frac{17 π}{12}$ is coterminal with $- \frac{41 π}{12}$ but isn\'t positive. Repeat the step.

$- \frac{17 π}{12}$

Add $2 π$ to $- \frac{17 π}{12}$ .

$- \frac{17 π}{12} + 2 π$

The resulting angle of $\frac{7 π}{12}$ is positive and coterminal with $- \frac{41 π}{12}$ .

$\frac{7 π}{12}$

Step 2

Since the angle $\frac{7 π}{12}$ is in the second quadrant, subtract $\frac{7 π}{12}$ from $π$ .

$π - \frac{7 π}{12}$

Step 3

Simplify the result.

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

$π \cdot \frac{12}{12} - \frac{7 π}{12}$

Combine fractions.

Combine $π$ and $\frac{12}{12}$ .

$\frac{π \cdot 12}{12} - \frac{7 π}{12}$

Combine the numerators over the common denominator.

$\frac{π \cdot 12 - 7 π}{12}$

Simplify the numerator.

Move $12$ to the left of $π$ .

$\frac{12 \cdot π - 7 π}{12}$

Subtract $7 π$ from $12 π$ .

$\frac{5 π}{12}$