Find the Reference Angle -(41pi)/4

$- \frac{41 π}{4}$

Step 1

Find an angle that is positive, less than $2 π$ , and coterminal with $- \frac{41 π}{4}$ .

Add $2 π$ to $- \frac{41 π}{4}$ until the angle falls between $0$ and $2 π$ . In this case, $2 π$ needs to be added $6$ times.

$- \frac{41 π}{4} + 6 (2 π)$

Simplify.

Multiply $2$ by $6$ .

$- \frac{41 π}{4} + 12 π$

To write $12 π$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{41 π}{4} + 12 π \cdot \frac{4}{4}$

Combine fractions.

Combine $12 π$ and $\frac{4}{4}$ .

$- \frac{41 π}{4} + \frac{12 π \cdot 4}{4}$

Combine the numerators over the common denominator.

$\frac{- 41 π + 12 π \cdot 4}{4}$

Simplify the numerator.

Multiply $4$ by $12$ .

$\frac{- 41 π + 48 π}{4}$

Add $- 41 π$ and $48 π$ .

$\frac{7 π}{4}$

Step 2

Since the angle $\frac{7 π}{4}$ is in the fourth quadrant, subtract $\frac{7 π}{4}$ from $2 π$ .

$2 π - \frac{7 π}{4}$

Step 3

Simplify the result.

To write $2 π$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$2 π \cdot \frac{4}{4} - \frac{7 π}{4}$

Combine fractions.

Combine $2 π$ and $\frac{4}{4}$ .

$\frac{2 π \cdot 4}{4} - \frac{7 π}{4}$

Combine the numerators over the common denominator.

$\frac{2 π \cdot 4 - 7 π}{4}$

Simplify the numerator.

Multiply $4$ by $2$ .

$\frac{8 π - 7 π}{4}$

Subtract $7 π$ from $8 π$ .

$\frac{π}{4}$