How do you find $tan (\frac{π}{3})$ $tan (pi/3)$ ?

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How do you find $tan (\frac{π}{3})$ $tan (pi/3)$ ?

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Answer 1 · 2014-10-24T22:00:27

Knowledge of special triangles is needed to solve this by hand.

$\frac{π}{3}$ $pi/3$ is $\frac{180^{\circ}}{3} = 60^{\circ}$ $180^circ/3=60^circ$

One of the special right triangles is $30^{\circ} 60^{\circ} 90^{\circ}$ $30^circ60^circ90^circ$ where the sides have lengths with the following ratios.

$30^{\circ} \Rightarrow x$ $30^circ => x$
$60^{\circ} \Rightarrow x \sqrt{3}$ $60^circ => xsqrt(3)$
$90^{\circ} \Rightarrow 2 x$ $90^circ => 2x$

If we let $x = 1$ $x=1$ then the side lengths are $1, \sqrt{3}, and 2$ $1, sqrt(3), and 2$ respectively.

$tan (θ) = \frac{o p p o s i t e}{a d j a c e n t} = \frac{y}{x}$ $tan (theta) = (opposite)/(adjacent) = y/x$

$tan (\frac{π}{3}) = \frac{\sqrt{3}}{1} = \sqrt{3}$ $tan(pi/3)=sqrt(3)/1=sqrt(3)$

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How do you find $tan (\frac{π}{3})$ $tan (pi/3)$ ?

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