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How do you calculate the #tan^-1(sqrt3/3)#?

1 Answer
Nov 25, 2015

Answer:

#pi/6#

Explanation:

Another way of asking this question is: "the tangent of what angle gives me #sqrt3/3#?"

We know that #" "tan(pi/6)=sqrt3/3#.

So then, #" "" "tan^-1(sqrt3/3)=pi/6#


Note that even though tangent is positive in the third quadrant, and that the tangent of an infinite amount of coterminal angles is #sqrt3/3#, we need to observe that the range of #tan^-1(x)# is #(-pi/2,pi/2)#, so only #pi/6# is a valid answer within this range.