Question

What is the cot(x) of x = -π (negative pi)?

Answer 1

y = 4 + cot(x) - 2csc(x)

y '(x) = -csc^2(x) + 2*csc(x)*cot(x) = 2*csc(x)*cot(x) - csc^2(x) =

csc(x) * [2*cot(x) - csc(x)]

Set equal to zero:

csc(x) * [2*cot(x) - csc(x)] = 0

csc(x) never equals zero.

[2*cot(x) - csc(x)] = 0

2*cos(x)/sin(x) - 1/sin(x) = 0

[2*cos(x) - 1] / sin(x) = 0

[2*cos(x) - 1] = 0 while sin(x) does not equal zero

cos(x) = 1/2

x = pi/3

y = 4 + cot(x) - 2csc(x)