Title: Sullivan Precalculus: Section 5.4 Graphing the Sine and Cosine Functions
1Sullivan 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
2The Graph of y sin x
y
x
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4Characteristics 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).
5Characteristics of the Sine Function
6Begin with the basic sine function
(0, 0)
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9The Graph of y cos x
y
x
10(0, 1)
11Characteristics 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).
12Characteristics of the Cosine Function
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14The graphs of the sine and cosine functions are
called sinusoidal graphs.
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161
-1
172
-2
18Find an equation for the graph.
4
3
2
-1
1
-4
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