Question

For finding the principal value,in this question:
Find the principal value of cot-1(-1/√3)
The answer is cot(π-π/3) which is cot (2π/3)
why is it not just -π/3?
In a similar question, Find the principal value of sin-1(-1/2), I tried doing sin(π+π/6) since sin is negative in 3rd quadrant.But the answer was just -(π/6).Why is there this difference?Someone please explain.Thank You

Answer 1

Don't be upset. It happens with most students. When I was a student it happened to me also.

First you need to know the domain of the function.

Cot works between 0 and +pi only. So principal value must like between them.
Again Sin lies between -pi/2 and +pi/2. So the principal value must like between that region.

Hope it helped you.