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Sullivan Algebra and Trigonometry: Section 6.6 Graphs of the Sine and Cosine Functions

Sullivan Algebra and Trigonometry: Section 6.6 Graphs of 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

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Sullivan Algebra and Trigonometry: Section 6.6 Graphs of the Sine and Cosine Functions

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  1. Sullivan Algebra and Trigonometry: Section 6.6Graphs of 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. (0, 0)

  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. The Graph of y = cos x y x

  8. (0, 1)

  9. 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).

  10. Characteristics of the Cosine Function

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

  12. 1 -1

  13. 2 -2

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

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