Question

find the reference angle for $\frac{11pi}{7}$. the reference angle is (simplify your answer. use integers or fractions for any numbers in the ex

Explanation:

Step1: Determine the quadrant

The angle $\theta=\frac{11\pi}{7}$. Since $2\pi=\frac{14\pi}{7}$ and $\frac{3\pi}{2}=\frac{21\pi}{14}$, $\frac{11\pi}{7}$ is in the fourth - quadrant as $\frac{3\pi}{2}>\frac{11\pi}{7}> \pi$.

Step2: Use the reference - angle formula for fourth - quadrant

For an angle $\theta$ in the fourth - quadrant, the reference angle $\theta_{r}=2\pi-\theta$.
Substitute $\theta = \frac{11\pi}{7}$ into the formula: $\theta_{r}=2\pi-\frac{11\pi}{7}=\frac{14\pi}{7}-\frac{11\pi}{7}=\frac{3\pi}{7}$.

Answer:

$\frac{3\pi}{7}$