Question

suppose an angle that measures \\(\theta = \frac{7\pi}{9}\\) radians is in standard position on the coordinate plane and \\(\
ho\\) is the measure of its reference angle. what is the value of \\(\
ho\\)?

Explanation:

Determine the quadrant of the angle

Using the Reference Angles knowledge point

$$ \frac{\pi}{2} < \frac{7\pi}{9} < \pi $$

The angle lies in Quadrant II.

Calculate the reference angle

Using the Reference Angles knowledge point

$$ ho = \pi - \theta = \pi - \frac{7\pi}{9} = \frac{2\pi}{9} $$

Answer:

\(\frac{2\pi}{9}\)