Question

If sin A = ${\displaystyle \frac{9}{41}}$ find all the values of cos A and tan A

Answer 1

We have sin A = ${\displaystyle \frac{9}{41}}$
As,
${\displaystyle {\mathrm{Cos}}^{2}A=1-{\sin }^{2}A}$

=${\displaystyle 1-{\left(\frac{9}{41}\right)}^2}$

=${\displaystyle 1-\frac{81}{1681}}$

=${\displaystyle \frac{1681-81}{1681}}$

${\displaystyle \Rightarrow {\cos }^{2}A=\frac{1600}{1681}}$

${\displaystyle \Rightarrow \cos A=\sqrt{\frac{1600}{1681}}}$

${\displaystyle \Rightarrow \cos A=\frac{40}{41}}$

Also, 

${\displaystyle \mathrm{Tan}A=\frac{\sin A}{\cos A}}$

${\displaystyle =\frac{\left(\frac{9}{41}\right)}{\left(\frac{40}{41}\right)}}$ 

${\displaystyle =\frac{9}{40}}$