How would I graph the function of sin(3/5x)?

Answer 1

I'm not exactly sure if you are referring to sin(3/(5x)) or sin((3/5)*x), but I'll go over both. For sin((3/5)*x) remember the sine pattern. sin(0)=0, sin(pi/2)=1, sin(pi)=0, etc. From here you can reverse these steps algebraically to match the x and y for your plot. So for the x value when pi/2=(3/5)*x, the sine will be 1. Essentially you are stretching the function out over the x axis.

Sin(3/(5x)) is a bit more complicated, but it's important to remember that there is a discontinuity at x=0. If you've discussed limits yet (sometimes taught in precalculus) the inner function would be approaching +infinity on the right and -infinity on the left. However, sin(+infinity) and sin(-infinity) do not exist since sine is an oscillating function. So as you get closer to x=0 the oscillations on sin(3/(5x)) are going to be shorter and shorter along the x-axis. It essentially becomes a blur as you approach 0. Hope that helped.