Sullivan Algebra and Trigonometry: Section 7.6

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Presentation transcript:

Sullivan Algebra and Trigonometry: Section 7.6 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

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).

Characteristics of the Sine Function

Begin with the basic sine function: (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).

Characteristics of the Cosine Function

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

1 -1

2 -2

Find an equation for the graph. 4 3 2 -1 1 -4