5.4 Graphs of the Sine and Cosine Functions

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Presentation transcript:

5.4 Graphs of the Sine and Cosine Functions

The Graph of y = sin x y x

(0, 0)

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). 4. 5.

Characteristics of the Sine Function 6.

Use the graph of to sketch the graph of

(0,0)

(0,0)

The Graph of y = cos x y x

(0, 1)

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). 4. 5.

Characteristics of the Cosine Function 6.

The graphs of the sine and cosine functions are called sinusoidal graphs.

Theorem

Find an equation for the graph.

Amplitude = 4 Period =T =2

Amplitude = 4 Period =T =2