csc(x)=3 and pi/2 less than (x) less than 3pi/2, find cot(x).
Then sin x = 1/3 and x is in quadrants II
I sketched a diagram, made my hypotenuse 3 and the opposite 1.
then the adjacent is √8, using Pythagoras
tan x = -1/√8
= -1/(2√2) or -√2/4 if rationalized.
To find cot(x), we first need to find the value of x. Given that csc(x) = 3 and pi/2 < x < 3pi/2, we can determine x by taking the inverse cosecant (csc^(-1)) of 3.
However, before we proceed, let's note that the range of csc(x) is between -∞ and -1, inclusive, and between 1 and ∞, inclusive. In this case, csc(x) = 3, which lies outside these ranges. Therefore, there is no solution for x, and as a result, cot(x) is undefined in this case.
If you had a different value for csc(x) that falls within the valid range, I would proceed with solving for x and then determining the cotangent value.