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4.5 Graphs of Sine and Cosine Functions

4.5 Graphs of Sine and Cosine Functions. Amplitude Period Translations. The graph of f(x)=sin x. Domain all Real numbers Range -1 to 1. The graph of f(x)=sin x. Sin x is an odd function. Graph of f(x) = -sin x. Graph of the f(x) = Cos x. Domain: All real numbers Range: -1 to 1.

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4.5 Graphs of Sine and Cosine Functions

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  1. 4.5 Graphs of Sine and Cosine Functions Amplitude Period Translations

  2. The graph of f(x)=sin x Domain all Real numbers Range -1 to 1

  3. The graph of f(x)=sin x Sin x is an odd function

  4. Graph of f(x) = -sin x

  5. Graph of the f(x) = Cos x Domain: All real numbers Range: -1 to 1

  6. Graph of the f(x) = Cos x Cos x is an even function

  7. The red graph is Sin and the blue is Cos

  8. Amplitude changes the Range

  9. Amplitude changes the Range Since Amplitude is a distance, it is always positive. To find it: the absolute value of the Maximum minus the Minimum divide by two. Amp is written before the function y = a*sin x

  10. Amplitude changes the Range Max 7; Min - 1 Amp.

  11. Period (wave length) The distance before the function repeats its value. y = sin bx; here b is 1.

  12. Period (wave length) y = sin 2x b = 2

  13. Translation to move the graph of the function y = sin (x + c): moves Right or Left Here is

  14. Translation to move the graph of the function y = sin x + d moves up or down Here is

  15. With all the translations The sine function is f(x) = d + a sin b(x +c) The cosine function is f(x) = d + a cos b(x +c)

  16. Applet for the Sine function • http://www.analyzemath.com/trigonometry/sine.htm

  17. Homework Page 307 – 310 # 3, 9, 14, 20, 26, 32, 41, 49, 71, 78

  18. Homework Page 307 – 310 # 7, 12, 17, 23, 27, 36, 45, 60, 76, 86

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