1. Chapter 5 Analytic Trigonometry 1

2. 5.3 Solving Trig Equations Objectives:  Use standard algebraic techniques to solve trigonometric equations.  Solve trigonometric equations of quadratic type.  Solve trigonometric equations involving multiple angles. 2

3. Solving Trig Equations  Use standard algebraic techniques such as collecting like terms and factoring.  Get the trig function alone on one side of the equation and then solve for the angle(s). 3

4. Example 1  Solve the equation. 4

5. Example 2  Find all solutions of the equation in the interval [0, 2π). 5

6. Example 3  Solve the equation. 6

7. Example 4  Solve the equation. (Hint: Get all terms on one side and factor.) 7

8. Example 5  Find all solutions of the equation in the interval [0, 2π). 8

9. Example 6  Solve the equation. 9

10. Example 7  Find all solutions of the equation in the interval [0, 2π). (Hint: Square each side of the equation and check for extraneous solutions.) 10

11. Example 8  Solve the equation. 11

12. Example 9  Solve the equation. 12

13. Example 10  Use your graphing calculator to approximate the solutions of the equation in the interval [–π, π]. 13

14. Example 11  The surface area of a honeycomb is given by the equation where h = 2.4 inches, s = 0.75 inch, and θ is the angle indicated in the figure. a. What value of θ gives a surface area of 12 square inches? b. What value of θ gives the minimum surface area? 14

15. Homework 5.3  Worksheet 5.3 15