Question

If cos∅=$\frac{1}{\sqrt{122} }$, then find tan∅.

Answer 1

SOLUTION

$cos \theta = \frac{</u><u>B</u><u>ase }{</u><u>H</u><u>ypotenuse} = \frac{1}{ \sqrt{122} } \\ \\ = > {</u><u>P</u><u>}^{2} = {</u><u>H</u><u>}^{2} - {</u><u>B</u><u>}^{2} \\ \\ = > {</u><u>P</u><u>}^{2} = ( { \sqrt{122} )}^{2} - ( {1)}^{2} \\ \\ = > {</u><u>P</u><u>}^{2} = 122 - 1 \\ \\ = > {</u><u>P</u><u>}^{2} = 121 \\ \\ = > </u><u>P</u><u> = \sqrt{121} \\ \\ = > </u><u>P</u><u> = 11cm \\ \\ now \\ = > tan \theta = \frac{</u><u>P</u><u>}{</u><u>B</u><u>} = \frac{11}{1} = 11cm$

Hope it helps ☺️

Answer 2

Step-by-step explanation:

$cos \alpha = \frac{1}{ \sqrt{122} } \\ {cos}^{2} \alpha = \frac{1}{122} \\ 1 - {sin}^{2} \alpha = \frac{1}{122} \\ {sin}^{2} \alpha = \frac{121}{122} \\ sin \alpha = \frac{11}{ \sqrt{122} } \:, \: \frac{ - 11}{ \sqrt{122} } \\ \\ tan \alpha = 11 \: , \: - 11 \\ If cosA is in first quadrant, then tanA is in first quadrant, hence positive & </p><p>if cosA is in fourth quadrant,</p><p> tanA is in fourth quadrant, hence tanA is negative value.\\ hope \: it \: willhelp \: you..$