10.4 Solving Trig Equations

Objectives:

1. Use identities to solve trig equations.

Methods for Solving

Remember, most trig equations can be solved two ways: By Graphing Algebraically

GraphingPros:

Can visually see solutions Good alternative if you hit a dead-end

when solving algebraicallyCons:

Usually need to convert decimal solutions to exact (with π)

No work to show, so can’t get partial credit for small mistakes.

AlgebraicallyPros:

Can find exact solutions Good practice using identities

Cons: Some equations are too messy

(have decimals, etc.)

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

Example 1:

Solve cos 2x = 1 – sin x for 0 ≤ x < 2π

Example 2:

Solve 3 cos 2x + cos x = 2 for 0 ≤ x < 2π

Example 3:

Solve 2 sin 2x = 1 for 0° ≤ x < 360°

You Try!

Solve cos 2x = cos x for 0° ≤ x < 360°

Example 4:

Find the smallest positive root of sin 2.8x = cos x