1. Graph of Secant, Cosecant, and Cotangent
Section 7.2
Pre-Calculus AB Pre-AP/Dual, Revised ©2014
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7.2: Graphs of Csc, Sec, and Cot Graphs

2. 7.2: Graphs of Csc, Sec, and Cot Graphs
Review
Revisit the Unit Circle
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7.2: Graphs of Csc, Sec, and Cot Graphs

3. 7.2: Graphs of Csc, Sec, and Cot Graphs
Review
Unit Circle of Sin Coordinates
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7.2: Graphs of Csc, Sec, and Cot Graphs

4. 7.2: Graphs of Csc, Sec, and Cot Graphs
Review
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7.2: Graphs of Csc, Sec, and Cot Graphs

5. 7.2: Graphs of Csc, Sec, and Cot Graphs
Quadrantals
From the Unit Circle, there are five points to graph.
Sine and Cosine graphs, they are 0, 𝝅 𝟐 , π, 𝟑𝝅 𝟐 , and 2π
Tan graphs are 0, 𝝅 𝟒 , 𝝅 𝟐 , 𝟑𝝅 𝟒 , and π
Cosecant graph is the reciprocal of a sine function, Secant graph is the reciprocal function, and Cotangent graph is the reciprocal of the tangent function
Asymptotes are all zeroes of the sine and graph
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7.2: Graphs of Csc, Sec, and Cot Graphs

6. 7.2: Graphs of Csc, Sec, and Cot Graphs
Review x
f(x)
π/2 π
3π/2 2π
f(x) 1 –1
Graph y = sin(x)
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7.2: Graphs of Csc, Sec, and Cot Graphs

7. 7.2: Graphs of Csc, Sec, and Cot Graphs
Example 1
Graph y = csc(x)
Radians
f(x)
π/2 π
3π/2 2π
Sin x 1 –1
1/Sin x
1/0
1/1
1/–1
1/Sin x
Und 1 –1
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7.2: Graphs of Csc, Sec, and Cot Graphs

8. 7.2: Graphs of Csc, Sec, and Cot Graphs
Example 1 x
f(x)
π/2 π
3π/2 2π
sin (x) 1 –1
Graph y = csc(x)
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7.2: Graphs of Csc, Sec, and Cot Graphs

9. 7.2: Graphs of Csc, Sec, and Cot Graphs
Radians
f(x)
π/2 π
3π/2 2π
sin x 1 –1
1/sin x
Und 1 –1
Example 1
Graph y = csc(x)
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7.2: Graphs of Csc, Sec, and Cot Graphs

10. 7.2: Graphs of Csc, Sec, and Cot Graphs
Example 1
Graph y = csc(x)
Period:
Domain:
Range:
Zeroes:
Odd or Even Function?
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7.2: Graphs of Csc, Sec, and Cot Graphs

11. 7.2: Graphs of Csc, Sec, and Cot Graphs
Example 1
Radians
π/2 π
3π/2 2π
csc x
Und. 1 –1
Graph y = csc(x)
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7.2: Graphs of Csc, Sec, and Cot Graphs

12. 7.2: Graphs of Csc, Sec, and Cot Graphs
Review
Unit Circle of Cosine Coordinates
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7.2: Graphs of Csc, Sec, and Cot Graphs

13. 7.2: Graphs of Csc, Sec, and Cot Graphs
Review
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7.2: Graphs of Csc, Sec, and Cot Graphs

14. 7.2: Graphs of Csc, Sec, and Cot Graphs
Example 2 x
f(x)
π/2 π
3π/2 2π
cos(x) 1 –1
Graph y = sec(x)
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7.2: Graphs of Csc, Sec, and Cot Graphs

15. 7.2: Graphs of Csc, Sec, and Cot Graphs
Radians
f(x)
π/2 π
3π/2 2π
cos x 1 –1
1/cos x 1
Und. –1
Example 2
Graph y = sec(x)
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7.2: Graphs of Csc, Sec, and Cot Graphs

16. 7.2: Graphs of Csc, Sec, and Cot Graphs
Radians
f(x)
π/2 π
3π/2 2π
1/cos x 1
Und. –1
Example 2
Graph y = sec(x)
Period:
Domain:
Range:
Zeroes:
Odd or Even Function?
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7.2: Graphs of Csc, Sec, and Cot Graphs

17. 7.2: Graphs of Csc, Sec, and Cot Graphs
Review
Unit Circle of Tangent Coordinates
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7.2: Graphs of Csc, Sec, and Cot Graphs

18. 7.2: Graphs of Csc, Sec, and Cot Graphs
Review
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7.2: Graphs of Csc, Sec, and Cot Graphs

19. 7.2: Graphs of Csc, Sec, and Cot Graphs
Radians
Tan y
π/4
π/2
3π/4 π
Tan x 1
Und. –1
1/tan x
1/0
1/1
1/und.
1/–1
Review
Unit Circle of Tangent Coordinates
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7.2: Graphs of Csc, Sec, and Cot Graphs

20. 7.2: Graphs of Csc, Sec, and Cot Graphs
Example 3
Radians
1/tan x
Und.
π/4 1
π/2
3π/4 –1 π
Graph y = cot(x)
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7.2: Graphs of Csc, Sec, and Cot Graphs

21. 7.2: Graphs of Csc, Sec, and Cot Graphs
Radians
f(x)
π/2 π
3π/2 2π
1/cos x 1
Und. –1
Example 3
Graph y = cot(x)
Period:
Domain:
Range:
Zeroes:
Odd or Even Function?
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7.2: Graphs of Csc, Sec, and Cot Graphs

22. 7.2: Graphs of Csc, Sec, and Cot Graphs
Example 3
Graph y = cot(x)
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7.2: Graphs of Csc, Sec, and Cot Graphs

23. 7.2: Graphs of Csc, Sec, and Cot Graphs
Assignment
Page odd
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7.2: Graphs of Csc, Sec, and Cot Graphs