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#