Question

solve for theta
sqrt3csc(theta)-2cot(theta)=0

Answer 1

this is a tough one
any ideas?

Answer 2

i cheated and looked up the answer
doesn't look like anything that will be easy to find
http://www.wolframalpha.com/input/?i=sqrt%283%29csc%28theta%29-2cot%28theta%29%3D0

Answer 3

i turned everything into terms of sine and cos and i just stared at it for a bit :/

Answer 4

haha that works too, thanks (:

Answer 5

well doesn't really explain much
it looks like it is cooked to be nice what with the \(\sqrt{3}\) and the \(2\)
like perhaps it is supposed to be the result of some double angle formula, but then when you see the answer....

Answer 6

\[ \begin{array}{rcr}
\sqrt{3}\csc(\theta)-2\cot(\theta) & = & 0 \\
\frac{\sqrt{3}}{\sin(\theta)}-\frac{2\cos(\theta)}{\sin(\theta)} & = & 0 \\
\sqrt{3}-2\cos(\theta) & = & 0 \\
2\cos(\theta) & = & \sqrt{3} \\
\cos(\theta) & = & \frac{\sqrt{3}}{2} \\
\theta & = & \frac{\pi}{6}
\end{array} \]
We assumed that \(\sin(\theta) \neq 0 \) as it would be undefined if that where true.
Also since \(\cos(\theta) \) is periodic, there are many solutions, I just gave the most obviou s one.

Answer 7

i guess this is what is asked for although apparently there are lots of other solutions

Answer 8

Consider\[\cos(\theta+2\pi n) = \cos(\theta) \quad n \in \mathbb{Z}\]And\[
\cos(-\theta) = \cos(\theta)
\]That is what I mean when I say there are many answers.