Question

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

Answer 1

I would suggest to go through direct calculations.
`sin(pi/3)=sqrt(3)/2`
Here `sqrt(3)/2` should be understood as an angle in radians.

Also notice that
`cot^-1(x)=tan(x)` (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,
`pi/180=0.866/X`

Therefore,
`X=180*0.866/pi~=49.6` (degrees)