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

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

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Answer 1 · 2015-08-16T12:38:03

$- \frac{1}{\sqrt{3}}$ $-1/sqrt(3)$

Explanation:

$tan (\frac{23 π}{6})$ $tan ((23pi)/6)$
$= tan (4 π - \frac{π}{6})$ $=tan (4pi - pi/6)$
$= \frac{tan (4 π) - tan (\frac{π}{6})}{1 + tan (4 π) tan (\frac{π}{6})}$ $=(tan(4pi) - tan(pi/6))/(1+tan(4pi)tan(pi/6))$
$= \frac{0 - \frac{1}{\sqrt{3}}}{1 + 0 (\frac{1}{\sqrt{3}})}$ $=(0-1/sqrt(3))/(1+0(1/sqrt(3)))$
$= - \frac{1}{\sqrt{3}}$ $=-1/sqrt(3)$

Answer 2 · 2015-08-16T12:55:38

Find $tan (\frac{23 π}{6})$ $tan ((23pi)/6)$

Ans: $- \frac{\sqrt{3}}{3}$ $- sqrt3/3$

Explanation:

$tan (\frac{23 π}{6}) = tan (- \frac{π}{6} + 4 π) = tan (- \frac{π}{6}) = - tan (\frac{π}{6}) = - \frac{\sqrt{3}}{3}$ $tan ((23pi)/6) = tan (-pi/6 + 4pi) = tan (-pi/6) = - tan (pi/6) = - sqrt3/3$

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

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