1 8.7 Trigonometric Equations (I) In this section, we will study the following topics: o Solving equations involving a single trig function algebraically. o Verifying the solutions of trigonometric equations graphically using the calculator.

2 Determine whether 60  is a solution of How many solutions does the equation have? In which quadrants would we find the solutions to this equation? Take a look at the graphs of

3 Solving trig equations with a restricted domain Often you are asked to solve a trigonometric equation over a given interval, most commonly on the interval, which equates to one revolution on the unit circle. Note: If the directions indicate that you are to solve the equation on the interval, then you should give your answers in radians. If the directions indicate that you are to solve the equation on the interval, then you should give your answers in degrees.

4 You can verify your solutions graphically using your calculator Enter the left side of the equation in Y1. Enter the right side of the equation in Y2. Adjust your window settings and graph both functions in the same window. Find the intersection points of the graphs. The x-values of the intersection points are the solutions to the equation.

5 Example

6

7

8

9 End of Section 8.7