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Question 150901: tan 11pi/6: tan 11pi/6
Answer by jim_thompson5910(9390) About Me  (Show Source):
You can put this solution on YOUR website!
Take note that pi/6+5pi/3=11pi/6


So

tan(11pi/6)=tan(pi/6+5pi/3)



tan(11pi/6)=(tan(pi/6)+tan(5pi/3))/(1-tan(pi/6)tan(5pi/3)) Use the Sum-Difference identity to rewrite the right side.


tan(11pi/6)=((sqrt(3)/3)-sqrt(3))/(1-(sqrt(3)/3)(-sqrt(3))) Using the unit circle, we get tan(pi/6)=sqrt(3)/3 and tan(5pi/3)=-sqrt(3)


tan(11pi/6)=((sqrt(3)/3)-sqrt(3))/(1-(-1)) Multiply sqrt(3)/3 and -sqrt(3) to get (sqrt(3)/3)(-sqrt(3))=-(sqrt(3)sqrt(3))/3=-3/3=-1


tan(11pi/6)=((sqrt(3)/3)-sqrt(3))/(2) Combine like terms in the denominator.


tan(11pi/6)=((sqrt(3)/3)-3sqrt(3)/3)/(2) Multiply -sqrt(3) by 3/3


tan(11pi/6)=(-2sqrt(3)/3)/(2) Combine the fractions in the numerator.


tan(11pi/6)=-sqrt(3)/3 Divide and simplify.



So the answer is tan(11pi/6)=-sqrt(3)/3