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