a Let's add the given angle, ∠ ROS, to the unit circle.
The number of degrees OR has rotated is given by ∠ SOR. Since this angle and ∠ ROS make a whole circle, 360^(∘), we can write the following equation.
∠ SOR+∠ ROS=360^(∘)
By substituting ∠ ROS=60^(∘), we can determine ∠ SOR.
b Examining the diagram, we see that △ ROS is a right triangle with a non-right angle of 60^(∘). This must mean that the second non-right angle is 30^(∘), which makes the triangle a 30^(∘)-60^(∘)-90^(∘) triangle. In such a triangle, the short leg is half the length of the hypotenuse and the long leg is sqrt(3) times greater than the short leg.
As we can see, the exact lengths of OS is 12, and the exact length of SR is 12sqrt(3).
c In Part B we calculated the exact length of OS and SR. Since OS is the horizontal distance between O and R and SR is the vertical distance between O and R, we can determine the exact coordinates of R. Notice that R is on the negative side of the y-axis, which means its y-coordinate must be negative.
