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Graphs of Sine and Cosine

Learn how to identify and graph periodic trigonometric functions. Explore translations, amplitude, phase shift, and vertical shift of sine and cosine functions. Practice graphing transformations accurately.

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Graphs of Sine and Cosine

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  1. Graphs of Sine and Cosine Essential Questions • How do we recognize and graph periodic and trigonometric functions? Holt McDougal Algebra 2 Holt Algebra 2

  2. Translations of Trigonometric Graphs Translation of a Sine Function Amplitude Period

  3. Translations of Trigonometric Graphs Translation of a Sine Function Amplitude Period Moving a graph left or right is called a phase shift.

  4. Amplitude Phase shift Vertical shift Period You can combine the transformations of trigonometric functions. Use the values of a, b, h, andkto identify the important features of a sine or cosine function. y =asinb(x–h)+k

  5. Translations of Trigonometric Graphs Draw one cycle of the function’s graph. Amplitude Period Translation down 2

  6. Translations of Trigonometric Graphs Draw one cycle of the function’s graph. Amplitude Period Translation up 3

  7. Translations of Trigonometric Graphs Draw one cycle of the function’s graph. Amplitude Period Translation right p

  8. Translations of Trigonometric Graphs Draw one cycle of the function’s graph. Amplitude Period Translation left p

  9. Translations of Trigonometric Graphs Draw one cycle of the function’s graph. Amplitude Period Translation right p/2

  10. Translations of Trigonometric Graphs Draw one cycle of the function’s graph. Amplitude Period Reflection over x-axis

  11. Translations of Trigonometric Graphs Draw one cycle of the function’s graph. Amplitude Period Reflection over x-axis

  12. Lesson 11.1 Practice B

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