Given sintheta=6/11 and sectheta>0, how do you find costheta, tantheta?

Aug 3, 2017

$\cos \theta = \frac{\sqrt{85}}{11}$ and $\tan \theta = \frac{6}{\sqrt{85}}$

Explanation:

As $\sin \theta$ and $\sec \theta$ both are positive $\theta$ lies $Q 1$ and hence all trigonometricratios of $\theta$ are positive.

$\cos \theta = \sqrt{1 - {\sin}^{2} \theta} = \sqrt{1 - {\left(\frac{6}{11}\right)}^{2}}$

$= \sqrt{1 - \frac{36}{121}} = \sqrt{\frac{85}{121}} = \frac{\sqrt{85}}{11}$

$\tan \theta = \frac{\frac{6}{11}}{\frac{\sqrt{85}}{11}} = \frac{6}{\sqrt{85}}$