1

What you will learn

How to solve trigonometric equations and inequalities

Objective: 7-5 Solving Trigonometric Equations

2

Solving Equations – Background Information

We are now going to start solving trigonometric equations…kind of like algebraic equations.

A little background:

- Most trig equations have more than one solution.

- Many trig expressions will take on a given value twice every period.

- If the variable is restricted to two adjacent quadrants, a trig equation will have fewer solutions.

- These solutions are called principal values.

- The principal values for sin and tan are in QI and QIV

- The principal values for cos are in Q1 and QII

Objective: 7-5 Solving Trigonometric Equations

3

Example

Solve: for principal values of x.

Express the solutions in degrees.

0cos2

1cossin xxx

Objective: 7-5 Solving Trigonometric Equations

4

You Try Solve: for

principal values of x. Express the solutions in degrees.

01sinsin2 2 xx

Objective: 7-5 Solving Trigonometric Equations

5

Another Example

Sometimes you may need to write the expression in terms of only one trig function. Example:

Solve: cos2x – cos x + 1 = sin2x for 20 x

Objective: 7-5 Solving Trigonometric Equations

6

You Try Solve: sin2x – sin x + 1 = cos2x for 20 x

Objective: 7-5 Solving Trigonometric Equations

7

And One More Thing… Most trig equations have infinitely many

solutions. When all values of x are required the solutions should be represented as for sin and cos and for tan

Example: Solve: 2 sec2x – tan4x = -1

kxkx o 2,360 kxkx o ,180

Objective: 7-5 Solving Trigonometric Equations

8

You Try Solve: 03cos32sin2sincos4 xxxx

Objective: 7-5 Solving Trigonometric Equations

9

Homework page 459, 17-21 odd, 23-27 odd, 31-35

odd, 37, 39, 55