Question

How would I solve each one to figure out the answer?

Answer 1

B. cos θ = -1/2

Step-by-step explanation:

To determine the equation in which the value of θ is a positive value, we solve each of the equations in radians:

`\begin{gathered} \tan \theta=-\frac{\sqrt[]{3}}{3}\implies\theta=\tan ^(-1)(-\frac{\sqrt[]{3}}{3})=-0.5236 \\ \cos \theta=-(1)/(2)\implies\theta=\cos ^(-1)(-(1)/(2))=2.0944 \\ \sin \theta=-\frac{\sqrt[]{3}}{2}\implies\theta=\sin ^(-1)(-\frac{\sqrt[]{3}}{2})=-1.0472 \\ \csc \theta=-1\implies-(\pi)/(2) \end{gathered}`

From the above, we see that only cos θ gives a positive value in radians.

The correct equation is B.