5.3 Subsection: Functions of Multiple Angles

This section deals with how to solve conditional, trigonometric equations that include TRIG(bx), where b does not equal 0 or 1.

Consider:

Solve for x in the interval

2cos(2x) = 1

First, isolate TRIG(bx)
cos(2x) = 1/2

Next, take the inverse cosine of both sides

This is not the end of the problem, however. Remember: The period of the function is 

In this case, the period is

As you can see by the graph, there are four solutions to the problem.

How do we get the other two?

Add the period to the solutions!

Add the period to each solution