## Finding Multiple Solutions of Trigonometric Equations

In general a trigonometric equation of the form for 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 or depending on whether we are working in degrees or radians. All the trigonometric graphs – sin, cos and tan – possess symmetry. All the graphs repeat every This means that if is a solution to a trigonometric equation, then will also be a solution for any integer n. However there are also specific rules for each function.

Example:

Solve  Since sin repeats every and is symmetrical about the lines  are also solutions.

The complete set of solutions is Solve  Since cos repeats every and is symmetrical about the lines  are also solutions.

The complete set of solutions is Solve  Since tan repeats every and is not symmetrical about any line are also solutions.

The complete set of solutions is #### Add comment Refresh