- #1
Dethrone
- 717
- 0
Find the points of intersection of $\rho=\cos\left({2\theta}\right)$ and $\rho=\cos\left({\theta}\right)$
By setting $\cos\left({2\theta}\right)=\cos\left({\theta}\right)$, we get the solutions $\theta=0,\frac{2\pi}{3},\frac{4\pi}{3}$.
My question is how come that doesn't give us all the points of intersection? There are some points of intersection at the poles that were not obtained above, such as $(0, \frac{\pi}{3})$ and $(0, \frac{\pi}{2})$
By setting $\cos\left({2\theta}\right)=\cos\left({\theta}\right)$, we get the solutions $\theta=0,\frac{2\pi}{3},\frac{4\pi}{3}$.
My question is how come that doesn't give us all the points of intersection? There are some points of intersection at the poles that were not obtained above, such as $(0, \frac{\pi}{3})$ and $(0, \frac{\pi}{2})$