Question

if tan theta = 1/2, find cos theta

Answer 1

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given

$\tan( \theta) = \frac{1}{2}$

in the above triangle ABC

AB=1,BC=2

finding AC by using Pythagoras theorem

we know that

${AC}^{2} = {AB}^{2} + {BC}^{2}$

$AC = \sqrt{ {AB}^{2} + {BC}^{2} } \\ AC = \sqrt{ {1}^{2} + {2}^{2} } \\ AC= \sqrt{1 + 4} \\ AC = \sqrt{5}$

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$\cos( \theta)$

$\cos( \theta) = \frac{adjacent}{hypotenuse}$

$\cos( \theta ) = \frac{2}{ \sqrt{5} }$

rationalize the denominator

$\cos( \theta) = \frac{2 \sqrt{5} }{5}$

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