Question

How do you graph to solve the equation on the interval `[-2pi,2pi]` for `cotx=-sqrt3/3`?

Answer 1

Solution : In interval `[-2pi,2pi] , x= -pi/3 = -60^0, x = -(4pi)/3=-240^0 x= (2pi)/3=120^0 , x = (5pi)/3=300^0`

Explanation:

`tan (pi/3) =3/sqrt3 :. cot (pi/3) =sqrt (3)/3 or cot (pi-pi/3) = -sqrt (3)/3`

`cot x = -sqrt (3)/3 :. x = (pi-pi/3) = (2pi)/3 ; x =pi+ (2pi)/3 = (5pi)/3`

`(5pi)/3 =((2pi)-(5pi)/3)= -pi/3 :. x = -pi/3;`

`(2pi)/3 =((2pi)-(2pi)/3)= -(4pi)/3 :. x = -(4pi)/3`

Solution : In interval `[-2pi,2pi] , x= -pi/3 = -60^0, x = -(4pi)/3=-240^0 x= (2pi)/3=120^0 , x = (5pi)/3=300^0`[Ans]