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How do you evaluate $arctan ((\frac{1}{\sqrt{3}})$ $arctan((1/sqrt3)$ ?

1 Answer

Jul 22, 2015

$arctan (\frac{1}{\sqrt{3}}) = \frac{π}{6} or 30^{o}$ $arctan(1/sqrt(3)) = pi/6 or 30^o$

Explanation:

This ratio is one of the standard trigonometric triangles:
enter image source here

$arctan$ $arctan$ must provide an angle in quadrants one or four; in quadrant four, the argument would have needed to be negative.

The ratio $\frac{(\frac{1}{2})}{(\frac{\sqrt{3}}{2})} = \frac{1}{\sqrt{3}}$ $((1/2))/((sqrt(3)/2)) = 1/sqrt(3)$
$XXXX$ $color(white)("XXXX")$ is that of a $\frac{π}{6}$ $pi/6$ angle (as indicated above).

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