Part 2/6:
To understand why this is the case, we can visualize it using a geometric approach. Imagine drawing a triangle on a coordinate plane, where one angle is y, and the other angle is x - y. You can label the sides of this triangle based on the cosine and sine definitions relative to the right angle.
In this triangle, if both sides are of length 1, the length equivalent to cos y can be represented on the x-axis, while sin y can represent the height. Similarly, cos x will determine how far along the axis we go when adding angles.
When you sum these distances, the right angle triangle's hypotenuse reflects how the two angles relate through this addition.
The Cosine Subtraction Formula
Next, we look at the cosine subtraction formula:
cos(x - y) = cos x * cos y + sin x * sin y