How do you graph #r=2sin3theta#?

1 Answer

Start with #y=sinx# then adjust.


First it's good to remember the basic graph of #y=sinx#:

graph{sinx [-6.25, 6.25, -2.2, 2.2]}

The graph spans #-2pi<=theta<=2pi#

Now let's make the needed adjustments.

First there's the 2. It is going to take the result of the sin function and increase it by a factor of 2. So the maximum and minimum on the y-axis will go from 1 to 2. That will look like this:

graph{2sinx [-6.25, 6.25, -2.2, 2.2]}

And now the #3theta#. This is going to make the result of any point along the x-axis compress in. For instance, at #theta=pi#, the function is going to return what we'd expect at #3pi#. This adjustment, without the first one we did for the 2, looks like this:

graph{sin(3x) [-6.25, 6.25, -2.2, 2.2]}

Put it all together and we get:

graph{2sin(3x) [-6.25, 6.25, -2.2, 2.2]}