# Find all solutions to the given equation in the interval [0,2π). Give the exact solution, including "pi" for π. 4cotx+4sqrt(3)=0?

### 5 Answers

- PinkgreenLv 76 months agoFavourite answer
4cot(x)+4sqr(3)=0, 0=<x<2pi

=>

tan(x)=-1/sqr(3)

=>

x=5pi/6, or x=11pi/6

- Wayne DeguManLv 76 months ago
4cotx + 4√3 = 0

so, cotx = -√3

i.e. tanx = -1/√3....negative means Q2

Then, x = -π/6 + nπ...for n = 0, 1, 2,...

or, x = (π/6)(6n - 1)

Hence, for n = 0 and 1 we have:

x = -π/6, 5π/6 and 11π/6

so, x = 5π/6 and 11π/6 are solutions for [0, 2π)

:)>

- VamanLv 76 months ago
4cotx+4sqrt(3)=0, cot x +sqrt 3=0, cot x +2 sqrt 3/2=0

cot x + 2 sin 60=0, 1/2 cos x/ sin x +sin 60=0

cos 60 sin x + sin 60 cos x=0

sin(x+60)=0= sin pi. pi= x+60, x= 180-60=120. This is the answer.

- Pramod KumarLv 76 months ago
Given --

4 cot x + 4 √3 = 0

Divide both the sides by 4 ---

=> cot x + √3 = 0

=> cot x = - √3

=> tan x = - ( 1/√3 )

tan has negative values in 2nd and 4th Quadrants.

=> x = (5/6) pi and (11/6) pi ................ Answer

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- ted sLv 76 months ago
cot Θ = - √3 has the reference triangle for Θ of { - √ 3 , 1 , 2 } for 2nd quadrant and { √3 , - 1 , 2 } for the 4th quadrant...5π / 6 and 11 π / 6