5.3 Solving Trigonometric Equations

1
5.3 Solving Trigonometric Equations
2
What are two values of x between 0 and

• When Cos x ½
• x arccos ½

3
How do you find

• What is the period of the Cosine function?

4
How to you find

• What is the period of the Cosine function?
• minus

5
Why does this work?

• Look at the Cosine function, there are many times
  it equals ½
• We limited it to 0 to

6
If we wanted all the answers to cos x ½

• The answers would be
• Where n is an integer

7
Solve for x

8
Solve for x

9
Solve for x for

10
Set each factor equal to 0

• Solve ( remember the period for tan is )

11
Set each factor equal to 0

• Solve ( remember the period for tan is )

12
When solving a trig equation, you must have only
one function

• Solve for x where the domain is

13
When solving a trig equation, you must have only
one function

• Solve for x where the domain is

14
When solving a trig equation, you must have only
one function

• Solve for x where the domain is

15
When solving a trig equation, you must have only
one function

• Solve for x where the domain is

16
When solving a trig equation, you must have only
one function

• Solve for x where the domain is

17
When solving a trig equation, you must have only
one function

• Solve for x where the domain is

18
Solve for x

• Let 2x u

19
Solve for x

• Let 2x u

20
Solve for x

• Let 2x u

21
Solve for y Domain

• Let sin y u

22
Solve for y Range

• Let sin y u

23
Solve for y

• Let sin y u

24
Solve for y domain

• We have to give all the answers

25
Solve for y domain

• We have to give all the answers

26
Homework

• Page 376 379
• 5, 9, 17, 22,
• 28, 35, 57,
• 61, 73

27
Homework

• Page 376 379
• 3, 7, 12, 20,
• 25, 31, 56,
• 60, 71, 87