Solving Trigonometric Equations

The basicandcurves are given on the left below andon the right below:

– blueblack

We have typically to solve equations such as

1. We start by making cosx the subject:

2. 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, 360-41.41, 360+41.41, 720-41.41, 720+41.41, 1080-41.41, 1080+41.41 ....degrees

Example: Solve

Now we use the symmetry of the sin curve. The solutions are

17.46, 180-17.46, 360+17.46, 540-17.46, 720+17.46,900-17.46 ....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