# If sinx=1/4 and tanx is positive, find cosx?

$\cos x = \frac{\sqrt{15}}{4}$
As $\sin x$ and $\tan x$ both are positive, $x$ lies in Quadrant 1 and $\cos x = \sin \frac{x}{\tan} x$ too is positive.
Hence, $\cos x = \sqrt{1 - {\sin}^{2} x} = \sqrt{1 - {\left(\frac{1}{4}\right)}^{2}} = - \sqrt{1 - \frac{1}{16}} = - \sqrt{\frac{15}{16}} = \frac{\sqrt{15}}{4}$