 # 4 5 Graphs of Sine and Cosine Functions

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Download presentation 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 Graph of the f(x) = Cos x is an even function The red graph is Sin and the blue is Cos Amplitude changes the Range 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 Amplitude changes the Range Max 7; Min - 1 Amp. Period (wave length) The distance before the function repeats its value. y = sin bx; here b is 1. Period (wave length) y = sin 2 x b = 2 Translation to move the graph of the function y = sin (x + c): moves Right or Left Here is Translation to move the graph of the functiony = sin x + d moves up or down Here is 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) Applet for the Sine function • http: //www. analyzemath. com/trigonometry/ sine. htm Homework Page 307 – 310 #3, 9, 14, 20, 26, 32, 41, 49, 71, 78 Homework Page 307 – 310 # 7, 12, 17, 23, 27, 36, 45, 60, 76, 86