Which value is a solution for the equation cotx/2=0

Question

Which value is a solution for the equation cotx/2=0

 

a) 3Π/4

b)3Π/2

c) Π/2

d)3Π

Answer 1

When is the cotangent of an angle equal to 0?

 

Since cot x = cos x / sin x, it occurs when cos x = 0.  That happens when x = π/2 and 3π/2, plus or minus all multiples of 2π.

 

One way to write that is π/2 ± 2πn and 3π/2 ± 2πn, where n is any integer.

 

In this problem, though, it's cot x/2 that's equal to 0, not cot x.

 

So that means that x/2 = π/2 ± 2πn or 3π/2 ± 2πn

 

Multiply both sides of this "equation" by 2:

 

x = π ± 4πn or 3π ± 4πn

 

Do any of the choices correspond to π ± 4πn or 3π ± 4πn?

 

Yes, (d) does.  When n = 0, 3π ± 4πn = 3π.  That's (d)