How do you evaluate $tan^-1(-(sqrt(3)/3))$ ?

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Answer 1 · 2016-02-20T05:13:39

We notice that for an angle $theta$ we have that

$tantheta=-sqrt3/3=-1/(sqrt3)=-(1/2)/(sqrt3/2)$

Now we need to find the angles $theta_1$ , $theta_2$ which have

$sintheta_1=-1/2$ and $costheta_1=sqrt3/2$

and

$sintheta_2=1/2$ and $costheta_2=-sqrt3/2$

These angles are $theta_1=150^o=5*pi/6$ and $theta_2=330^o=11*pi/6$

How do you evaluate tan^-1(-(sqrt(3)/3))tan^-1(-(sqrt(3)/3))?