1. 1 What you will learn  How to solve trigonometric equations and inequalities

2. Objective: 7-5 Solving Trigonometric Equations 2 Solving Equations – Background Information We are now going to start solving trigonometric equations…kind of like algebraic equations. A little background: - Most trig equations have more than one solution. - Many trig expressions will take on a given value twice every period. - If the variable is restricted to two adjacent quadrants, a trig equation will have fewer solutions. - These solutions are called principal values. - The principal values for sin and tan are in QI and QIV - The principal values for cos are in Q1 and QII

3. Objective: 7-5 Solving Trigonometric Equations 3 Example Solve: for principal values of x. Express the solutions in degrees.

4. Objective: 7-5 Solving Trigonometric Equations 4 You Try  Solve: for principal values of x. Express the solutions in degrees.

5. Objective: 7-5 Solving Trigonometric Equations 5 Another Example  Sometimes you may need to write the expression in terms of only one trig function. Example: Solve: cos 2 x – cos x + 1 = sin 2 x for

6. Objective: 7-5 Solving Trigonometric Equations 6 You Try  Solve: sin 2 x – sin x + 1 = cos 2 x for

7. Objective: 7-5 Solving Trigonometric Equations 7 And One More Thing…  Most trig equations have infinitely many solutions. When all values of x are required the solutions should be represented as for sin and cos and for tan  Example: Solve: 2 sec 2 x – tan 4 x = -1

8. Objective: 7-5 Solving Trigonometric Equations 8 You Try  Solve:

9. Objective: 7-5 Solving Trigonometric Equations 9 Homework  page 459, 17-21 odd, 23-27 odd, 31-35 odd, 37, 39, 55