How do you make a sin graph with a period of 4pi?

1 Answer
Gió
Oct 24, 2015

I would manipulate the numerical coefficient inside the argument of the sine:

Explanation:

If you have the normal sine function (period#=2pi#):
#y=sin(x)#
the coefficient conected with the period is the #1# multiplying the argument as in: #y=sin(x)=sin(1*x)#;
this coefficient (call it #c#) helps you to "see" the period of your function that can be evaluated as:
#period=(2pi)/c=(2pi)/1=2pi#

Now if you want a period of #4pi# you need that #c=1/2# so that you get:
#period=(2pi)/c=(2pi)/(1/2)=2pi*2=4pi~~12.6rad#

Finally the complete function will be:

#y=sin(c*x)=sin(1/2x)#

and graphically:
graph{sin(1/2x) [-18.02, 18.03, -9.01, 9.01]}

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