Sullivan Precalculus: Section 5.4 Graphing the Sine and Cosine Functions - PowerPoint PPT Presentation

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Sullivan Precalculus: Section 5.4 Graphing the Sine and Cosine Functions

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Sullivan Precalculus: Section 5.4 Graphing the Sine and Cosine Functions Objectives of this Section Graph Transformations of the Sine Function Graph Transformations ... – PowerPoint PPT presentation

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Title: Sullivan Precalculus: Section 5.4 Graphing the Sine and Cosine Functions


1
Sullivan Precalculus Section 5.4Graphing the
Sine and Cosine Functions
  • Objectives of this Section
  • Graph Transformations of the Sine Function
  • Graph Transformations of the Cosine Function
  • Determine the Amplitude and Period of Sinusoidal
    Functions
  • Graph Sinusoidal Functions y Asin(wx)
  • Find an Equation for a Sinusoidal Graph

2
The Graph of y sin x
y
x
3
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4
Characteristics of the Sine Function
1. The domain is the set of all real numbers.
2. The range consists of all real numbers from -1
to 1, inclusive.
3. The sine function is an odd function
(symmetric with respect to the origin).
5
Characteristics of the Sine Function
6
Begin with the basic sine function
(0, 0)
7
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9
The Graph of y cos x
y
x
10
(0, 1)
11
Characteristics of the Cosine Function
1. The domain is the set of all real numbers.
2. The range consists of all real numbers from -1
to 1, inclusive.
3. The cosine function is an even function
(symmetric with respect to the y-axis).
12
Characteristics of the Cosine Function
13
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14
The graphs of the sine and cosine functions are
called sinusoidal graphs.
15
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1
-1
17
2
-2
18
Find an equation for the graph.
4
3
2
-1
1
-4
19
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