## Solving Multiple Angle Trigonometric Equations

It is quite easy to find an answer for the equationfor example. We finddegrees. However this is not the only answer. Because of the periodicity of the cosine curve, repeating every 360 ^{o } and symmetry of the cosine curve aboutetc, the following are also solution:

Suppose instead we have to solve the equation

Now we can write down lots of equations to solve, again using the symmetry of the cosine curve:

Normally we are given a range in which the values ofmust lie. If the range is in this case 0-360 ^{o }, then is this case only the first four values ofwould be the required solutions.

Example: Find all the solutions ofin the range 0 ^{o }-360 ^{o }.

The graph of sin has symmetry in the lineswe have

sodegrees.

degrees.

degrees.

degrees.