Question

Which value is a solution for the equation cot (x/2) = 1 ?

A. 5π/2
B. 7π/4
C. π/4
D. 3π/4

Answer 1

I know that x = 1/2 (4π n+π) ..... but what does that mean?

Answer 2

\( \cot x = \dfrac{1}{\tan x} \)

If \( \cot \frac{x}{2} = 1\)

then \( \dfrac{1}{\tan \frac{x}2{}} = 1 \)

and \( \tan \frac{x}{2} = 1 \)

Where is tan x = 1?

Answer 3

x = 1/4 (4 π n+π)
So does that mean it is C. ?

Answer 4

\( \tan \theta = 1\) at \( \theta = \dfrac{\pi}{4} \)

\(\tan \frac{x}{2} = 1 \)

\( \dfrac{x}{2} = \dfrac{\pi}{4} \)

\( x = \dfrac{\pi}{2} \)

Answer 5

Nvm. Cant be! Must be A.

Answer 6

Since the tangent function is a cyclical function, any multiple of \(2 \pi \) you add to it is also a solution.
x = 1/2 (4π n+π) = \( 2 \pi n + \dfrac{\pi}{2} \), for all integers, n.
There you see the pi/2 of our solution plust the \(2 \pi n \) part which is all the other solutions.
All you need to do is see which choice is a multiple of \(2 \pi \) added to \( \dfrac{\pi}{2} \)

Answer 7

Correct. It's A.