1.17.08 General Trig Equations

Trigonometric Equations

0sincossin2

2

2sin

92tan3

Trigonometric Equations

When we solve an equation such as

we must be sure to include all possible solutions.

It may very be the case that we disregard most of these, but it is important to know what they are.

21cos2

Steps for Solving a Trigonometric Equation:

1. Isolate the trig. function

2. Use an inverse trig. function to find one solution.

3. Use the unit circle to find a second solution (usually).

4. Use the periodicity of the function to state the general solution to the equation.

For example:

1. Isolate the trig. function.

2. Use an inverse trig. Function to find the first solution.

3. Use the unit circle to find a second solution.

4. Use the periodicity of the function to state the general solution.

2

1cos

21cos2

32

1cos 1

3

5or

3

.integer any for 23

5or 2

3nnn

1

0.8

0.6

0.4

0.2

-0.2

-0.4

-0.6

-0.8

-1

-1 -0.5 0.5 1

Try these:

2

2sin .1

92tan3 .2