Question

find the reference angle for $\frac{7pi}{12}$. the reference angle is . (simplify your answer. use integers or fractions for any numbers in the expression. type you)

Explanation:

Step1: Determine the quadrant

Since $\frac{\pi}{2}=\frac{6\pi}{12}<\frac{7\pi}{12}<\pi=\frac{12\pi}{12}$, the angle $\frac{7\pi}{12}$ is in the second - quadrant.

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

For an angle $\theta$ in the second - quadrant, the reference angle $\theta_{r}=\pi-\theta$. Here $\theta = \frac{7\pi}{12}$, so $\theta_{r}=\pi-\frac{7\pi}{12}$.

Step3: Calculate the reference angle

$\pi-\frac{7\pi}{12}=\frac{12\pi}{12}-\frac{7\pi}{12}=\frac{5\pi}{12}$.

Answer:

$\frac{5\pi}{12}$