Trigonometry is the study of triangles and angles. It discusses topics like the unit circle, quadrants, trig functions of sine, cosine and tangent, angle measures in degrees and radians, and trig identities. The unit circle is used to find trig function values of angles, with the radius being 1 and angles measured by coordinates (x,y) or (sin,cos). There are also discussions on converting between degree and radian measures, initial and terminal angles, reciprocal trig functions, and Pythagorean identities relating trig functions.