How do you evaluate cot ((7pi)/6)?

1 Answer
Konstantinos Michailidis
Jul 9, 2016

It is

cot((pi+6pi)/6)=cot(pi+pi/6)=cot(pi/6)=sqrt3

Another way is that

cot(pi+pi/6)=1/(tan(pi+pi/6))

Use the tan(a + b) = [tan a + tan b]/[1 - (tan a)(tan b)]

so you get:

tan(pi + pi/6) = [tanpi + tanpi/6]/[1 - (tanpi)(tanpi/6)] = [ 0 + (sqrt3)/3] / [1 - (0)((sqrt3)/3)] = [(sqrt3)/3] / [1 - 0] = [(sqrt3)/3] / 1 = [sqrt3] / 3

Hence cot(pi+pi/6)=1/(sqrt3/3)=sqrt3

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