Question

If sin θ = 1 over 3 and tan θ < 0, what is the value of cos θ? (1 point)

Answer 1

$\sin\theta=\dfrac13>0$, so

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

Recall that

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

for all $\theta$, and knowing that $\cos\theta$ we have

$\cos\theta=-\sqrt{1-\sin^2\theta}=-\dfrac{2\sqrt2}3$