What's a degree? In trigonometry, a degree is a tiny slice of a circle. Imagine a pizza cut into 360 equal pieces (what a mess). Each little slice represents one degree.
The first quadrant is the upper right-hand corner of the coordinate plane. That first quadrant is 1/4 of the entire plane. So, if a full circle with its center at the origin has a total of 360 degrees, then 1/4 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. The most frequently used angle measures include
And then, twice the 30-degree angle is 60 degrees (another common angle in trig).
This elite group of angle measures is 0, 15, 30, 45, 60, and 90 degrees. These angles and their multiples occupy much of the discussion in trigonometry because of their convenience in computations.
