1. 8.1: Graphical Solutions of Trig Functions
Worksheet 3 Key 1)
–π/2 2)
2π/3 3)
–π/6 4)
–π/4 5) –1 6) 7)
3/2 8)
𝟏𝟕 𝟏𝟕 9) 𝟏𝟎
10)
–π/3
11)
𝟐 𝟐
12)
𝟐 𝟑 𝟑
13) 1
14)
Undef
15) 2
16)
3/4
17)
12/13
18)
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8.1: Graphical Solutions of Trig Functions

2. Graphical Solutions of Trig Functions
Section 8.1
Pre-Calculus AB PreAP/Dual, Revised ©2014
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8.1: Graphical Solutions of Trig Functions

3. Types of Trigonometric Functions
Identities
sin2x + cos2x = 1
1 + tan2x = sec2x
1 + cot2x = csc2x
Conditional Equations
Equations that are true for certain values
sin x = 0
cos x = ½
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8.1: Graphical Solutions of Trig Functions

4. 8.1: Graphical Solutions of Trig Functions
Steps
Put the equation into y= form
In graphing calculator, it is necessary to change graphing windows
Use 2nd trace 5, enter, enter, enter to find intersection points
Round answers to 4 decimal places and add 2πk (sin, cos, sec, csc) or πk (cot, tan)
Special Instructions: When the equation says sin2x, put in calculator as (sin x)2
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8.1: Graphical Solutions of Trig Functions

5. 8.1: Graphical Solutions of Trig Functions
Example 1
Solve sin x = –0.75 from (0, 2π)
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8.1: Graphical Solutions of Trig Functions

6. 8.1: Graphical Solutions of Trig Functions
Example 2
Solve cos x = from (0, 2π)
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8.1: Graphical Solutions of Trig Functions

7. 8.1: Graphical Solutions of Trig Functions
Example 3
Solve csc x = 1.45 from (0, 2π)
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8.1: Graphical Solutions of Trig Functions

8. 8.1: Graphical Solutions of Trig Functions
Your Turn
Solve sin x = 0.33 from (0, 2π)
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8.1: Graphical Solutions of Trig Functions

9. 8.1: Graphical Solutions of Trig Functions
Example 4
Solve tan x – 3sin 2x = 0
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8.1: Graphical Solutions of Trig Functions

10. 8.1: Graphical Solutions of Trig Functions
Example 5
Solve 3sin2 x = cos x + 2
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8.1: Graphical Solutions of Trig Functions

11. 8.1: Graphical Solutions of Trig Functions
Your Turn
Solve 4cos2 x + sin x – 2 = 0
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8.1: Graphical Solutions of Trig Functions

12. 8.1: Graphical Solutions of Trig Functions
Assignment
Page odd, odd Go to dangmath.com to download a graphing calculator on the phone:
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8.1: Graphical Solutions of Trig Functions