Graphing polar equation $r\sin \theta = 1$?

Question

How would you graph $r \sin \theta = 1$?

I know that $r\sin \theta$ is equal to $y$, but the place where I'm told to graph this function on is a polar graph. How should I go about this?

Answer 1

While Milo is correct about this particular graph, let me pretend it isn't that easy so as to give you an idea how to proceed with this in general:

$(x, y) = (r\cos \theta, r\sin \theta)$, and the equation you want to graph is $r \sin \theta = 1$ which solves to $r = 1/\sin \theta$. so: $$(x, y) = \left(\frac{\cos \theta}{\sin \theta}, \frac{\sin \theta}{\sin \theta}\right) = (\tan \theta, 1)$$

Now, choose various values of $\theta$, and plot the corresponding points $(x, y)$, and there is your graph. (Okay, I'm old-school. This is how you plot it by hand.)

Answer 2

Note that equation can be rewritten as $\ r = \dfrac{1}{\sin \theta}$.
Therefore you can explicitly compute the value of $r$ for each value of $\,\theta$, except for $\theta = \pi n$, in which case you can compute a limit.

For example, for $\theta=\pi/2$ you get $r = 1$, for $\theta=\pi/3$ $r = 2/\sqrt{3}$, for $\theta=3\pi/4$ $r = \sqrt{2}$, etc.