Question

if tan theta+4/5=5,find sin theta and cos theta

Answer 1

Let theta be
$\alpha$
$\tan( \alpha ) + \frac{4}{5} = 5$
$\tan( \alpha ) = 5 - \frac{4}{5}$
$\tan( \alpha ) = \frac{21}{5}$
We know
$\tan( \alpha ) = \frac{opp}{adj}$
$\sin( \alpha ) = \frac{opp}{hyp}$
$\cos( \alpha ) = \frac{adj}{hyp}$
Where
$hyp = \sqrt{ {opp}^{2} +{adj^{2} } }$
Therefore hyp from above formula is
$hyp = \sqrt{ {21}^{2} + {5}^{2} }$
$hyp = \sqrt{ 441 + 21 }$
$hyp = \sqrt{466}$
$\sin( \alpha ) = \frac{21}{ \sqrt{466} }$
$\cos( \alpha ) = \frac{5}{ \sqrt{466} }$