I'm trying to find the angle of intersection between two polar curves:
$$\begin{cases}r= 5 + 3 \sin\theta \\ r' = 3\end{cases}$$
I've set them as $5 + 3\sin\theta = 3$ and got to $\sin\theta = -2/3$ but from here how do I find $\theta$? The unit circle seems useless here. Can someone please teach me the way?
Thanks
Best Answer
$$\sin \theta = -\frac 23 \iff \arcsin (\sin \theta) = \arcsin\left(-\frac 23\right) \iff \theta =\arcsin\left(-\frac 23\right)$$
You'll need to approximate $\theta$, since there is no "nice" angle $\theta$ such that $\sin(\theta)=-\frac 23$.