As a goodbye to sines and cosines, we can add one more piece to the puzzle. Understanding how to calculate sin and cos with the simple 0,1,2,3,4 trick (as described in episode 24), and how this relates to the unit circle, i.e. the x-coordinate being the cosine value and the y-coordinate being the sine value of the angle w/r/t (with respect to) the positive axis, is the bulk of the material.
If one can understand cartesian coordinate quadrants, it adds another dimension to your arsenal. Our Cartesian Coordinate Axes can be divided into four quadrants. Starting with upper right quadrant, called the first quadrant, we will begin to move counter-clockwise around the coordinate axes. These quadrants also correspond to 90 degree increments of the unit circle.
The upper right quadrant is an area which has only positive values for both the x and y values. This means that FROM 0-90 DEGREES BOTH SINE AND COSINE ARE POSITIVE.
The upper left quadrant is referred to as the SECOND quadrant. In the second quadrant y-values remain positive and x-values are negative. This means that FROM 90-180 DEGREES SINE IS POSITIVE AND COSINE IS NEGATIVE.
The lower left area is known as the THIRD quadrant. In this area both x- and y-values are negative. This means that FROM 180-270 DEGREES SINE AND COSINE ARE BOTH NEGATIVE.
The lower right area is known as the FOURTH quadrant. In this area the x-values are positive while the y-values are negative. This means that from 270-360 DEGREES SINE IS NEGATIVE AND COSINE IS POSITIVE.
This is illustrated in some detail in the picture below. Combine these tools together and you will have be at a great advantage when calculating vector components, and understanding where those confusing sines and cosines come from in later courses!
