Given $cosalpha=1/3$ , how do you find $cotalpha$ ?

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Given $cosalpha=1/3$ , how do you find $cotalpha$ ?

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Answer 1 · 2016-12-19T14:40:31

$sqrt2/4$

Explanation:

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

$cot t = cos t/(sin t) = (1/3)(3/(2sqrt2))= 1/(2sqrt2) = (sqrt2)/4$ .

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Given $cosalpha=1/3$ , how do you find $cotalpha$ ?

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