It is quite easy to find an answer for the equation
for example. We find
degrees. 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 about
etc, 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 of
must 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 of
in the range 0 o -360 o .
The graph of sin has symmetry in the lines
we have
so
degrees.
degrees.
degrees.
degrees.