# sec theta=3, sin theta>0 Find sin theta

$\mathrm{sec}\theta =3,\mathrm{sin}\theta >0$
Find $\mathrm{sin}\theta$
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gwibdaithq

since $\mathrm{sec}\theta =3>0$ is positive and is in Quadrant I.
We know that:
$\mathrm{sec}\theta =\frac{hyp}{opp}=\frac{3}{1}$
So
$\left(opp{\right)}^{2}+\left(adj{\right)}^{2}=\left(hyp{\right)}^{2}$
$\left(opp{\right)}^{2}+{1}^{2}={3}^{2}$
$\left(opp{\right)}^{2}+1=9$
$\left(opp{\right)}^{2}=8$
$opp=\sqrt{8}=\frac{2}{\sqrt{2}}$
Hence
$\mathrm{sin}\theta =\frac{opp}{hypp}$
$\mathrm{sin}\theta =2\frac{\sqrt{2}}{3}$