# How do you evaluate cot^-1 (sin (pi/3))?

Apr 27, 2015

I would suggest to go through direct calculations.
$\sin \left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2}$
Here $\frac{\sqrt{3}}{2}$ should be understood as an angle in radians.

Also notice that
${\cot}^{-} 1 \left(x\right) = \tan \left(x\right)$ (by definition of $\tan$ and $\cot$)

So, we have to evaluate
tan(sqrt(3)/2 radians) ~= tan(0.866 radians)~=1.176

By the way, $0.866$ radians is approximately $49.6$ degrees, if that better illustrates a problem. Transformation from radians to degrees is simple.
It's known that $\pi$ radians is $180$ degrees.
Assume that $0.866$ radians is $X$ degrees.
So,
$\frac{\pi}{180} = \frac{0.866}{X}$

Therefore,
$X = 180 \cdot \frac{0.866}{\pi} \cong 49.6$ (degrees)