Question

determine the reference angle, in radians, associated with the given angle. write the exact answer. do not round.

\\(\theta = \frac{15\pi}{14}\\)

Explanation:

Step1: Determine the quadrant

The angle $\theta=\frac{15\pi}{14}$ is between $\pi$ and $\frac{3\pi}{2}$ since $\pi=\frac{14\pi}{14}$ and $\frac{3\pi}{2}=\frac{21\pi}{14}$. So it is in the third - quadrant.

Step2: Use the reference - angle formula for third - quadrant angles

For an angle $\theta$ in the third quadrant, the reference angle $\theta_{r}=\theta-\pi$.
$\theta_{r}=\frac{15\pi}{14}-\pi=\frac{15\pi}{14}-\frac{14\pi}{14}=\frac{15\pi - 14\pi}{14}=\frac{\pi}{14}$

Answer:

$\frac{\pi}{14}$