Question

find points of intersection for the curves r=cot(x) and r=2cos(x)

Answer 1

i got :
\[x = \frac{\pi}{6}, \frac{5\pi}{6}\]

Answer 2

thanks that's what i got also.
i guess the answer key is wrong

Answer 3

bah i forgot the obvious answers <.< the statement is also true when cos(x) = 0. That gives us two more answers:
\[x = \frac{\pi}{2}, \frac{3\pi}{2}\]

Answer 4

I guess i should have solved it like this:
\[\frac{\cos(x)}{\sin(x)} = 2\cos(x) \Leftrightarrow \cos(x) = 2\sin(x)\cos(x) \Leftrightarrow 0 = 2\sin(x)\cos(x)-\cos(x)\]
\[0 = \cos(x)(2\sin(x)-1)\]
So then you can see that either cos(x) = 0, or 2sin(x)-1 = 0, and that gives you all four answers.