In week 15 of precalc we started going into trigonometry. This meant stuff like rotation angles and triangles. It’s usually finding the length of one side or the angle of two sides of a triangle using Sine, Cosine and Tangent. To review on how it works, there’s an abbreviation called SOH CAH TOA. Basically it means Sine = Opposite/Hypotenuse (SOH), Cosine= Adjacent/Hypotenuse (CAH) and Tangent = Opposite/Adjacent (TOA).

Now when we have a point on a graph it has its own rotation angle to what is known as the starting arm. In Trig, you try to find the angle between the two arms. You can have more than one arm on a graph, and they can have the same REFERENCE ANGLE but have different ROTATION ANGLES. The reference angle is in the first quadrant and can be used to find the rotation angle of other arms, for example if you have an arm in the first and third quadrants, you can add 180 to the rotation angle and that will be the rotation angle of the arm in Q3, for example the Rotation angle of 45 in Q3 is 225 because 45+180=225. For another example, the reference angle of 348 is 12 because 360-348=12.

As another way to explain it, you either add or subtract the reference angle from the closest horizontal arm, depending on the position of the terminal arm to find the rotation angle.