This document discusses two methods for solving trigonometric equations: graphing and algebraically. Graphing allows for visually seeing solutions but may result in decimal answers, while algebraic solving provides exact solutions but can become messy. It provides tips for algebraic solving based on whether the equation contains functions of 2x and x, or only 2x. Examples are given to demonstrate each method.

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 π)
No work to show, so can’t 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 < 2π

7. Example 2:
 Solve 3 cos 2x + cos x = 2 for 0 ≤ x < 2π

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