Answer
(a) Refer to the image below for the drawing.
(b) $\dfrac{13}{6}\pi$ radians
(c) Reference angle = $30^o$ or $\dfrac{\pi}{6}$ radians.
Work Step by Step
(a) From the positive x-axis, move 390 degrees counter clockwise. Note that the terminal side of this angle is the same as the terminal side of a 30-degree angle.
(refer to the attached image above for the drawing)
(b) Convert to radians by multiplying $\dfrac{\pi}{180^o}$ to obtain:
$390^o \cdot \dfrac{\pi}{180^o} = \dfrac{13}{6}\pi$ radians
(c) The angle is in Quadrant I as it is coterminal with $30^o$. The reference angle of an angle $\theta$ in Quadrant I is itself.
Thus, the reference angle of the given angle is:
$\color{blue}{30^o}=30^o \cdot \dfrac{\pi}{180^o}=\color{blue}{\dfrac{\pi}{6}}$ radians.
