1. 10.4 Solving Trig Equations Objectives: 1. Use identities to solve trig equations.
2. Methods for Solving Remember, most trig equations can be solved two ways: By Graphing Algebraically 3. Graphing Pros: Can visually see solutions Good alternative if you hit a dead-end when solving algebraically Cons: Usually need to convert decimal solutions to exact (with ) No work to show, so cant get partial credit for small mistakes. 4. Algebraically Pros: Can find exact solutions Good practice using identities Cons: Some equations are too messy (have decimals, etc.) 5. Solving Tips (Algebraic) If equation has functions of 2x and x: Use identities to rewrite using functions of x If equation has functions of 2x only: Solve for 2x directly, then divide to find x 6. Example 1: Solve cos 2x = 1 sin x for 0 x < 2 7. Example 2: Solve 3 cos 2x + cos x = 2 for 0 x < 2 8. Example 3: Solve 2 sin 2x = 1 for 0 x < 360 9. You Try! Solve cos 2x = cos x for 0 x < 360 10. Example 4: Find the smallest positive root of sin 2.8x = cos x