Question

find the reference angle for the given angle.
(a) $\frac{5pi}{6}$
(b) $\frac{10pi}{9}$
(c) $\frac{23pi}{7}$

Explanation:

Step1: Identify quadrant for $\frac{5\pi}{6}$

$\frac{5\pi}{6}$ is in QII.

Step2: Calculate reference - angle for $\frac{5\pi}{6}$

$\pi-\frac{5\pi}{6}=\frac{\pi}{6}$

Step3: Identify quadrant for $\frac{10\pi}{9}$

$\frac{10\pi}{9}$ is in QIII.

Step4: Calculate reference - angle for $\frac{10\pi}{9}$

$\frac{10\pi}{9}-\pi=\frac{\pi}{9}$

Step5: Identify quadrant for $\frac{23\pi}{7}$

$\frac{23\pi}{7}=3\pi+\frac{2\pi}{7}$, so it is in QIII.

Step6: Calculate reference - angle for $\frac{23\pi}{7}$

$\frac{23\pi}{7}-3\pi=\frac{2\pi}{7}$

Answer:

(a) $\frac{\pi}{6}$
(b) $\frac{\pi}{9}$
(c) $\frac{2\pi}{7}$