Question

find the reference angle for $\frac{7pi}{10}$. the reference angle is $square$. (simplify your answer. use integers or fractions for any numbers in the expression. type your answer in radians.)

Explanation:

Step1: Determine the quadrant

The angle $\theta=\frac{7\pi}{10}$ is in the second - quadrant since $\frac{\pi}{2}<\frac{7\pi}{10}<\pi$.

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

For an angle $\theta$ in the second quadrant, the reference angle $\theta_{r}=\pi-\theta$.
So, $\theta_{r}=\pi - \frac{7\pi}{10}$.

Step3: Calculate the reference angle

$\pi-\frac{7\pi}{10}=\frac{10\pi}{10}-\frac{7\pi}{10}=\frac{3\pi}{10}$.

Answer:

$\frac{3\pi}{10}$