I am looking to find out how to graph the above referenced function.
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If you're used to thinking of degrees rather than radians, then remember that (pi) radians=180 degrees, so (pi)/4=45, (pi)/2=90, (pi)/6=30. And, since sin(0)=sin(180)=sin(360)=sin(540)=sin(720)=0, then sin(0)=sin((pi))=sin(2(pi))=sin(3(pi))=sin(4(pi))=0, and so on. This is the same as putting x=0, 1/2, 1, 3/2 in the function. These are the zeroes, and they repeat forwards and backwards (positive and negative) along the x axis at these regular intervals of 1/2. When we have sin((pi)/2)=sin(90)=1, x=(pi)/4(pi)=1/4. 3sin(2(pi)x) when x=1/4 is 3; sin(3(pi)/2)=-1, and x=3(pi)/4(pi)=3/4, so 3sin(2(pi)x) when x=3/4 is -3. The sine curve oscillates between 3 and -3 (amplitude) cutting the x axis at the above zeroes. To help draw the curve accurately it's useful to find out a few other points: for example sin(30)=sin((pi)/6)=1/2 and x=(pi)/12(pi)=1/12 and y=3/2 or 1.5; also y=3/2 when x=5/12 because sin(5(pi)/6)=sin((pi)/6)=1/2. When deciding on a scale for the axes you might consider subdivisions of 1/12 along the x axis between the units 0, 1, 2, 3, etc. these will make it easier to pinpoint 1/12 and 5/12 and other such values.

by Top Rated User (1.2m points)

Given graph the function y=3 sin 2 pi x

It is a straight line graph

Click here for graph

 

by Level 8 User (30.1k points)
edited by

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