How do you find the exact value of #sin(tan^-1(sqrt3/3))#?

1 Answer
Binayaka C.
Oct 11, 2016

The exact value of #sin(tan^-1(sqrt3/3)) =1/2#

Explanation:

#sin(tan^-1(sqrt3/3))#. Let #tan^-1(sqrt3/3)=theta :. tan theta=sqrt3/3#
We know #tantheta#= perpendicular/base=#sqrt3/3 :.#Hypotenuse #= sqrt(3^2+(sqrt3^2))= sqrt12=2sqrt2 :. sin theta=#perp./hypotenuse #=sqrt3/(2sqrt3)=1/2 :.theta=sin^-1(1/2)#
Hence #sin(tan^-1(sqrt3/3)) = sin(sin^-1(1/2))=1/2# [Ans]

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