Question

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

Answer 1

`\sin\theta=\frac13>0`, so

`\tan\theta=(\sin\theta)/(\cos\theta)<0\implies\cos\theta<0`

Recall that

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

for all
`\theta`, and knowing that
`\cos\theta<0` we have

`\cos\theta=-√(1-\sin^2\theta)=-\frac{2\sqrt2}3`