### 16.5. Solving a Trigonometric Equation

We will now use our ability to manipulate trigonometric functions to solve trigonometric equations. But first we will solve trigonometric equations graphically and then by calculator.

▪ Exploration:

Try this. Use your calculator to graph the trigonometric function

- y = 2 sinx + 1

in degrees, for x = −50° to + 700°.

Earlier when you graphically found roots of equations, what did you look for? Do you see any roots here? Where, approximately? Can you list all the roots? Why or why not?

Graph of y = 2 sin x + 1. Tick marks on the x axis are 90° apart.

In your exploration, you probably found that the given equation has an infinite number of roots, both positive and negative. However, it is customary to list only nonnegative values of the roots, and only those between 0° and 360°.

TI-83/84 screen for Example 27: , showing roots at 30° and 150°. We have used the zero feature to locate the root at x = 30°. Tick marks on the x axis are 90° apart.

#### 16.5.1. Graphical Solution of Trigonometric Equations

In an earlier chapter, we used a graphics calculator or a graphing utility on the computer to get an approximate solution to an algebraic equation. Here we ...