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4.5 Graphs of Sine and Cosine Functions

Explore amplitude, period, translations, and properties of sine and cosine functions. Learn how to calculate amplitude and understand the impact of translations on graphs. Access an applet for visualizing sine functions and practice problems.

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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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