Solving Trigonometric Equations
The basicandcurves are given on the left below andon the right below:
– blueblack
We have typically to solve equations such as

We start by making cosx the subject:

We take the inverse cos:
Now is the tricky part. There is more than one solution forWe have found one. The other solutions are given by using the symmetry of the cosine graph. It is symmetric about 180 We are using degrees here. The solutions are
41.41, 36041.41, 360+41.41, 72041.41, 720+41.41, 108041.41, 1080+41.41 ....degrees
Example: Solve
Now we use the symmetry of the sin curve. The solutions are
17.46, 18017.46, 360+17.46, 54017.46, 720+17.46,90017.46 ....degrees
Example: Solve
Now we we the property of the tan curve that it repeats every 180 degrees. The solutions are
60.26, 180+60.26, 360+60.26, 540+60.26, 720+60.26, 900+60.26.....degrees