# How do you use sintheta=1/3 to find sectheta?

Feb 19, 2018

$\sin \theta = \frac{1}{3}$

by the identity, we know, ${\cos}^{2} x + {\sin}^{2} x = 1$

therefore, ${\sin}^{2} \theta = 1 - {\cos}^{2} \theta$

${\cos}^{2} \theta = 1 - {\left(\frac{1}{3}\right)}^{2}$

${\cos}^{2} \theta = 1 - \left(\frac{1}{9}\right)$

${\cos}^{2} \theta = \frac{8}{9}$

$\cos \theta = \pm \sqrt{\frac{8}{9}} = \pm \frac{2 \sqrt{2}}{3}$

now, we know, secθ=1/costheta

secθ=+-3/(2sqrt2)