How to graph this sin equation?

Question

I have the following sin equation which I am supposed to graph: sin(3x) = -1 and also find how many solutions it contains between 0 and 2π. Seeing this I am a bit confused as I don't understand what I am supposed to do with the -1. Usually when I graphed these they just equaled y. This said this is what I tried:

A (amplitude): 1

B (the stretch/compression amount): 3

P (the period): $\frac{2\pi}{3}$

Note: I found the period by doing $\frac{2\pi}{B}$

Should I bring the -1 on the other side of the equation and let it act as the axis of the wave / mid-line?

Basically my question is: what should I do with the -1? How does it affect the graph?

Answer 1

You can think of it also as, Where do $y=\sin{(3x)}$ and $y=-1$ intersect.

Answer 2

You should graph $y = \sin(3x) + 1$ and look at the points where $y = 0$, i.e. the points where the graph crosses the y-axis.

Edit: As Edward Jiang pointed out in the comments, the above is technically incorrect. You are asked to graph $\sin(3x) = -1$. Hence, to find the values of $x$ that solve this equation, just graph $y = \sin(3x)$ and find the points where the graph crosses the line $y = -1$. However, what I wrote above will give the same answers.