Solving Trigonometric Equations

The basicandcurvesare given on the left below andonthe 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 solutionforWehave found one. The other solutions are given by using the symmetryof the cosine graph. It is symmetric about 180 We are using degreeshere. 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 solutionsare

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 repeatsevery 180 degrees. The solutions are

60.26, 180+60.26, 360+60.26, 540+60.26, 720+60.26,900+60.26.....degrees