CPM Homework Help : CCA2 Problem 7-55

The measure of $∠ROS$ in $ΔROS$ below is $60^\circ$ .

Unit circle, center at origin, labeled, o, with right triangle, whose hypotenuse is segment from the circle center, to point, r, on circle in fourth quadrant, horizontal leg, from, o, to s, on positive x axis, & vertical leg, from s, to r. A curved counter clockwise arrow, from positive x axis, to the hypotenuse.

The curved arrow represents the rotation of $\overline { O R }$ , beginning from the positive $x$ -axis. Through how many degrees has $\overline { O R }$ rotated?
Hint (a):
Remember that a whole circle is $360^\circ$ .
If $OR = 1$ , what are the exact length of $OS$ and $SR$ ?
Hint (b):
Remember the $30^\circ-60^\circ-90^\circ$ triangle.
What are the exact coordinates of point $R$ ?
Answer (c):
$\left(\text{cos}(300^{^{\circ}}), \text{sin}(300^{^{\circ}})\right)\text{ or }\left(\frac{1}{2}, - \frac{\sqrt{3}}{2}\right)$