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Sine and Cosine Graphs in Algebra and Trigonometry

Learn about graph transformations, amplitude, period, and equations of sinusoidal functions like y = Asin(wx) and explore characteristics of sine and cosine functions.

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Sine and Cosine Graphs in Algebra and Trigonometry

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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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