Multiple Solutions of Trigonometric Equations

In general a trigonometric equation of the formfor example may have more than one solution, and may have in fact an infinite number of solutions. We often have to find the solutions within a certain range eg 0 – 360 o ordepending on whether we are working in degrees or radians. All the trigonometric graphs – sin, cos and tan – possess symmetry.

All the graphs repeat everyThis means that ifis a solution to a trigonometric equation, thenwill also be a solution for any integer n. However there are also specific rules for each function.

Example:

Solve

Since sin repeats everyand is symmetrical about the lines

are also solutions.

The complete set of solutions is

Solve

Since cos repeats everyand is symmetrical about the lines

are also solutions.

The complete set of solutions is

Solve

Since tan repeats everyand is not symmetrical about any lineare also solutions.

The complete set of solutions is