How do I find the value of $cot (- 240^{o})$ $cot(-240^o)$ ?

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How do I find the value of $cot (- 240^{o})$ $cot(-240^o)$ ?

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Answer 1 · 2015-08-12T12:25:35

$cot (- 240^{o}) = \frac{\sqrt{3}}{3}$ $cot(-240^o) = sqrt(3)/3$

Explanation:

$- 240^{o}$ $-240^o$ is equivalent to $120^{o}$ $120^o$

A $120^{o}$ $120^o$ is in Quadrant II with a reference angle of $60^{o}$ $60^o$

$60^{o}$ $60^o$ is a standard angle with $tan (60^{o}) = \sqrt{3}$ $tan(60^o) = sqrt(3)$
$XXXX$ $color(white)("XXXX")$ $XXXX$ $color(white)("XXXX")$ $XXXX$ $color(white)("XXXX")$ $\to cot (60^{o}) = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3}$ $rarr cot(60^o) = 1/sqrt(3) = sqrt(3)/3$

In Quadrant II, $tan$ $tan$ (and, therefore, $cot$ $cot$ ) is negative,

so
$XXXX$ $color(white)("XXXX")$ $cot (- 240^{o}) = - \frac{\sqrt{3}}{3}$ $cot(-240^o) = -sqrt(3)/3$

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How do I find the value of $cot (- 240^{o})$ $cot(-240^o)$ ?

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How do I find the value of $cot (- 240^{o})$ $cot(-240^o)$ ?