How do you graph #y=sin(1/4x)#?

1 Answer

Answer:

Start with the basic sine graph, then expand it by a factor of 4

Explanation:

With any question regarding graphing, we should first know the basic shape of the function. This is #y=sinx# from #(-2pi, 2pi)#

graph{sinx [-6.25, 6.25, -1.1, 1,1]}

Now let's bring in the #1/4#. What will that do to the function? It means that for any value, say #x=pi#, it will be evaluated as if it was #x=pi/4# and so it will expand the period of the function by a factor of 4, like this:

graph{sin(x/4) [-6.25, 6.25, -1.1, 1,1]}