# How to graph this sin equation?

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?

• Just graph $y=\sin(3x)$, then find the points where the $y$-coordinate is $-1$. The problem was badly stated – Edward Jiang Jan 4 '15 at 2:21
• The edit made to the question kind of changes things... – turkeyhundt Jan 4 '15 at 2:23
• @turkeyhundt the edit completely changed my problem. I am not sure why it was made. – Cristian Gutu Jan 4 '15 at 2:24

You can think of it also as, Where do $y=\sin{(3x)}$ and $y=-1$ intersect.
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.
• Oh, I misread the question. Sorry! However, this will give equivalent values for $x$. – Mark Jan 4 '15 at 2:28
• The graph is shifted one unit up. It gives equivalent values of $x$, but the graph is wrong. – Edward Jiang Jan 4 '15 at 2:30