Question

If sin theta = 2/3 and tan theta <0 what is the value of cos theta?

Answer 1

Answer:

d) $\cos(\theta)=-\frac{\sqrt{5}}{3}$

Step-by-step explanation:

If   $\sin(\theta)=\frac{2}{3}$ and $\tan(\theta)\:$, then

$\theta$ is in quadrant 2.

Recall that;

$\sin^2(\theta)+\cos^2(\theta)=1$

We substitute the given sine ratio to obtain;

$(\frac{2}{3})^2+\cos^2(\theta)=1$

$\frac{4}{9}+\cos^2(\theta)=1$

$\cos^2(\theta)=1-\frac{4}{9}$

$\cos^2(\theta)=\frac{5}{9}$

$\cos(\theta)=\pm \sqrt{\frac{5}{9}}$

$\cos(\theta)=\pm \frac{\sqrt{5}}{3}$

We are in the second quadrant, therefore

$\cos(\theta)=-\frac{\sqrt{5}}{3}$