Question

How do you evaluate the equation `arctan( -sqrt3 / 3 )`?

Answer 1

Converting the question in EQUATION FORM :
`color(red)(x)=arctan(-(sqrt3)/3)=-pi/6`

Explanation:

`color(red)((1)tan^(-1)(-X)=-tan^-1(X),X in R`
`color(red)((2)tan(pi/6)=1/sqrt3`.
`color(red)((3)tan^(-1)(tan(X))=X,AA X in(-pi/2,pi/2))`
If the equation is, `color(red)(x)=tan^(-1)(-(sqrt3)/3)`, then applying (1) we get `x=-tan^(-1)((sqrt3)/3)=-tan^(-1)(1/sqrt3)`, now from (2) we get`x=-tan^(-1)(tan(pi/6)),where,pi/6 in(-pi/2,pi/2)`
`x=-pi/6 to` [ Applying (3) ]