3.7 Trig Equations

Warm-up (IN)1. Solve:

2. Find the exact value of:

Learning Objective: to identify numerous solutions to trig equations, understand the procedure to locate the solutions using appropriate visual cues, and develop number sense with extensive use of fractions.

3 5 1x x

a. sin _______4

8b. cos _______

3

3

2x

2

2

1

2

Ex 1 – Determine whether the following are solutions to the equation 1

sin2

a. =4

sin4

1

2

No!

b. =6

sin6

1

2

Yes!

Ex 2 – Solve . List 8 solutions1

cos2

3

5

3

2k

What is the period for cos?

So… 6

3 3

7

3

13

3

5

3

11

3

5 6

3 3

11

3

1

3

Ex 3 – Solve the equations on the interval

a. 2sin 3 0

2sin 3 3

sin2

4

3

5and

3

0 2

General formula

1b. sin 2

2 We know where

sin=1/2 6

5and

6

So… 2 6

2k

2 5

6

2k

12

5

12

But…there are more π/12s that work!

So, use the general formula…

2 6

k

12

12

12

13

12

2 5

6

k 5

12

12

12

17

12

c. tan 12

We know where tan=1 4

5and

4

2

4

3

4

2

5

4

7

4

So…

Ex 4 – Solve using calculator

sin 0.3 We can use 2nd sin, but that would only give us one answer and we need all of them between 0 and 2π

So, graph it…but don’t forget to change to radians! And, change your window

.30x

2.84x

HW – 272 #7-12,25,27,31,32,41-43,53,54

Out – solve

Summary – I think I understand…

Don’t forget about POW!!Toys for Tots!

2sin 1 0