Given pi2

Given pi/2<x<pi and sinx=3/5 calculate cotx.

We notice that the angle x is located in the 2nd quadrant, therefore the values of cotangent function are negative.

We know that cot x = cos x/sin x

We\'ll determine cos x, applying the Pythagorean identity:

(cos x)^2 + (sin x)^2 = 1

(cos x)^2 = 1 - (sin x)^2

(cos x)^2 = 1 - 9/25

(cos x)^2 = (25 - 9)/25

(cos x)^2 = 16/25

cos x = -4/5

We\'ll keep only the negative value for cos x, since x is in the second quadrant and cosine function is negative.

cot x = (-4/5)/(3/5)

cot x = -4/3

The value of cotangent function is: cot x = -4/3.