General Solution of Trigonometric Equations

Measurement of angles in radians and degrees

In the radian system of angular measurement, the measure of one revolution is 2π.

Half a circle, then, is π. And, most important, each right angle is half of π i.e. 

Three right angles will be 3. 

Five right angles will be  and so on

Radians into degrees

The following radian measures come up frequently, and the student should know their degree equivalents:

 is half of , a right angle, and so it is equal to 45°.

 is one-third of π, and so is equal to 180°/ 3 = 60°.

 is one-sixth of π, and so is equal to 180°/ 6 = 30°.

 = 5.  = 5 x 45° = 225°

 is one-third of 2π, and so is equal to one-third of a revolution i.e. 360°/ 3 = 120°.