Why is the period of trig equations important when solving trig equations?

Answer 1

Trigonometric equations often have infinitely many solutions, due to the periodicity of the functions. Take a simple example, sin x = 0. This equation is satisfied by an angle of zero, but also by an angle of pi, 2 x pi, 3 x pi, etc. (this is in radians; the equivalent in degrees would be 0°, 180°, 360°, etc.). Once you find two base solutions (in this case 0 and pi), repeatedly adding the length of the period (in this case, 2 pi, equivalent to 360°) will give you additional solutions.