Today's soundtrack is Our Lady Peace: Clumsy, a unique, grungy album by the Canadian alt-rock band.
I've already learned about angles in standard position in the first quadrant; I'm now learning about how we can work with angles in any quadrant on a graph.
There are four quadrants in a graph. The origin of the graph is where x 0 and y 0 meet. The quadrants ascend counter-clockwise - another thing that makes no sense. The first quadrant is the northeast quadrant; the second quadrant is the northwest quadrant; the third quadrant is the southwest quadrant, and the fourth quadrant is the southeast quadrant.
Any of the four quadrants can contain angles. Any angles that are in the second, third, or fourth quadrants are measured in two ways: the angle and the reference angle. The angle is simply how many degrees are measured from the positive x arm swung around to the terminal arm. The reference angle is the measure of the "acute angle that the terminal arm makes with the x-axis" (Pearson's Pre-Calculus 11, p. 441). Angles in the first quadrant are their own reference angles.
If we are given the angle and want to find the reference angle, we do so by subtraction:
Quadrant 1: The angle is the reference angle.
Quadrant 2: Subtract the angle from 180 to get the reference angle.
Quadrant 3: Subtract 180 from the angle to get the reference angle.
Quadrant 4: Subtract the angle from 360 to get the reference angle.
That's all for today!