finding csc given sin 
$\sin \theta= -\frac{3}{7}$.
Find $\csc\theta$.

I don't get it, is $x$ or $r$ the negative?
There just doesn't seem to be enough information given.
 A: $\sin$ is a function which takes any real argument, so in general you don't really need to think of it in terms of triangles.
But let's say that you want to think of it exclusively in terms of triangles, so that $\sin(\theta)$ is defined as follows: draw a right triangle with angle $\theta$; then $\sin(\theta)$ equals the length of the opposite side divided by the length of the hypothenuse; if we place the adjacent side on the positive $x$-axis, then length is taken to be "positive" if it goes to the right or up, and negative if it goes left or down. Then, it doesn't matter if you are considering the opposite side or the radius to be "negative", what matters is:


*

*The value of $\sin\theta$; and

*The relationship between $\sin\theta$ and $\csc\theta$.


Remember that, as long as $\sin\theta\neq 0$, then you have that
$$\csc\theta = \frac{\text{hypothenuse}}{\text{opposite}} = \frac{1}{\quad\frac{\text{opposite}}{\text{hypothenuse}}\quad} = \frac{1}{\sin\theta}.$$
So, since you know what $\sin\theta$ is, how much is $\csc\theta$?
