How do I evaluate tan(23pi/6) without using a calculator?

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Answer 1 · 2015-08-16T12:38:03

#-1/sqrt(3)#

#tan ((23pi)/6)#
#=tan (4pi - pi/6)#
#=(tan(4pi) - tan(pi/6))/(1+tan(4pi)tan(pi/6))#
#=(0-1/sqrt(3))/(1+0(1/sqrt(3)))#
#=-1/sqrt(3)#

Answer 2 · 2015-08-16T12:55:38

Find #tan ((23pi)/6)#

Ans: #- sqrt3/3#

#tan ((23pi)/6) = tan (-pi/6 + 4pi) = tan (-pi/6) = - tan (pi/6) = - sqrt3/3#