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

1 Answer
Apr 27, 2015

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)