Sounds like you are on the right track.
Be careful on how you enter your equations into Wolfram. Its best to have some understanding of Mathematica when using this tool.
To find the x-intercepts (or theta intercepts!) solve
How do I graph y=1+2sin6theta?
What I got so far is that the 1 makes everything shift up
2 makes the amplitude 2 times bigger
so the amplitude would be from 3 to -1
the six theta would compress everything by a factor of six
so all the x intercepts would be factors of pi/6 instead of pi
however, when I enter this equation into Wolfram|Alpha: Computational Knowledge Engine the intercepts were shifted to the right of pi/6
what transformation did I miss?