Given $cos α = \frac{1}{3}$ $cosalpha=1/3$ , how do you find $cot α$ $cotalpha$ ?

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Given $cos α = \frac{1}{3}$ $cosalpha=1/3$ , how do you find $cot α$ $cotalpha$ ?

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Answer 1 · 2016-12-19T14:40:31

$\frac{\sqrt{2}}{4}$ $sqrt2/4$

Explanation:

$cos t = \frac{1}{3}$ $cos t = 1/3$ . Find sin t.
${sin}^{2} t = 1 - {cos}^{2} t = 1 - \frac{1}{9} = \frac{8}{9}$ $sin^2 t = 1 - cos^2 t = 1 - 1/9 = 8/9$ --> $sin t = \pm \frac{2 \sqrt{2}}{3}$ $sin t = +- (2sqrt2)/3$
Since cos t = 1/3, t is in Quadrant I, then sin t is positive.

$cot t = \frac{cos t}{sin t} = (\frac{1}{3}) (\frac{3}{2 \sqrt{2}}) = \frac{1}{2 \sqrt{2}} = \frac{\sqrt{2}}{4}$ $cot t = cos t/(sin t) = (1/3)(3/(2sqrt2))= 1/(2sqrt2) = (sqrt2)/4$ .

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Given $cos α = \frac{1}{3}$ $cosalpha=1/3$ , how do you find $cot α$ $cotalpha$ ?

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Given $cos α = \frac{1}{3}$ $cosalpha=1/3$ , how do you find $cot α$ $cotalpha$ ?