4.5 Graphs of Sine and Cosine Functions AmplitudePeriodTranslations

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 Cos x is an even function

The red graph is Sin and the blue is Cos

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 2x b = 2

Translation to move the graph of the functiony = 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 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