Question

if sin theta =3/7 and tan theta <0 what is the value of cos theta

Answer 1

Remember that

$\tan\theta=\dfrac{\sin\theta}{\cos\theta}$

So if $\sin\theta>0$ and $\tan\theta<0$, then we know $\cos\theta<0$.

Then use the Pythagorean identity to solve for cosine:

$\cos^2\theta+\sin^2\theta=1\implies\cos\theta=-\sqrt{1-\sin^2\theta}=-\dfrac{2\sqrt{10}}7$