The Most Frequently Used Trig Angles
There are certain angles that you will use frequently when you work with trigonometry functions. You can find these angles by cutting a graph into four parts, and then dividing those parts into smaller ones.
If you cut a graph into four parts, by tradition, the upper right-hand corner of the coordinate plane is labeled as being the first quadrant. That first quadrant is one-quarter of the entire plane. The other quadrants are then labeled, moving counter-clockwise.
So if a full circle with its center at the origin has a total of 360 degrees, then one-quarter of it has 90 degrees, which is the measure of the angle that the first quadrant forms. Actually, each quadrant measures exactly 90 degrees.
You can divide each of these 90-degree measures evenly by many numbers, and you use those equal divisions frequently in trig, because they’re nice, neat divisions.
This elite group of angle measures is 90, 60, 45, 30, 15, and 0 degrees.
These angles and their multiples occupy much of the discussion in trigonometry because of their convenience in computations. The above figure shows sketches of some of the angles.