Hello, Glitch!

I have the following function:

. .

$\displaystyle y \:=\: \dfrac{\cos x}{1 - \sin x}$ where $\displaystyle x = \frac{\pi}{6}$

Say I solve this for $\displaystyle y$, and I get the solution 1.73205

I happen to know this is $\displaystyle \sqrt{3}$,

but if I didn't, is there an intuitive way to make this connection?

It seems to be bad form to express it as a decimal.

We're expected to know about the 30-60 right triangle.

Code:

*
* 60*
2 * *
* * 1
* *
* 30 *
* * * * _ * * *
√3

Hence, we have: .$\displaystyle \begin{Bmatrix} \sin30^o &=& \sin\frac{\pi}{6} &=& \dfrac{1}{2} \\ \\[-3mm] \cos30^o &=& \cos\frac{\pi}{6} &=&\dfrac{\sqrt{3}}{2} \\ \\[-3mm] \tan30^o &=& \tan\frac{\pi}{6} &=& \dfrac{1}{\sqrt{3}} \end{Bmatrix}$

So we have: .$\displaystyle y \;=\;\dfrac{\cos\frac{\pi}{6}}{1-\sin\frac{\pi}{6}} \;=\;\dfrac{\frac{\sqrt{3}}{2}}{1 - \frac{1}{2}} \;=\;\dfrac{\frac{\sqrt{3}}{2}}{\frac{1}{2}} \;=\;\sqrt{3}$