1. 6.5 Solving Trig Equations & Inequalities

2. Technique #1  Factoring Ex 1) Solve
We will solve trigonometric equations & inequalities by combining algebraic techniques & trig identities
There are lots of techniques! Keep in mind if the answer must be in a specified interval.
Technique #1  Factoring
Ex 1) Solve
Note: If no interval had been specified, the answer would be:

3. Technique #2  Expressing in terms of only 1 trig function
Note: Remember if you square both sides of an equation – you might create extra “solutions.” Be sure to check your answers!
Ex 2) Solve

4. Technique #3  Think about the period!
Ex 3) Solve
0 ≤ 3x < 6π
(3 revs!)

5. Technique #4  Approximating answers (radian mode) Ex 4) Solve
1.91
ref ∠ = π – 1.91
= 1.23

6. Technique #5  Inequalities where [0, 2π]
Ex 5) Solve