Question

question
find the reference angle for a rotation of \frac{10\pi}{9}.
answer
attempt 1 out of 3
submit answer
watch video
show examples

Explanation:

Step1: Determine the quadrant

Since \(\frac{10\pi}{9}\) is in the third quadrant (\(\pi<\frac{10\pi}{9}<\frac{3\pi}{2}\)).

Step2: Calculate the reference angle

The formula for the reference angle \(\theta_{ref}\) of an angle \(\theta\) in the third quadrant is \(\theta_{ref}=\theta - \pi\).
Substitute \(\theta=\frac{10\pi}{9}\) into the formula: \(\theta_{ref}=\frac{10\pi}{9}-\pi=\frac{10\pi - 9\pi}{9}=\frac{\pi}{9}\)

Answer:

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