Question

If theta lies in the third quadrant and sin 0 = - 4/7, what is the value of cos theta?

Answer 1

`-\frac{\sqrt[]{33}}{7}`

Explanation:

We have that being in the third quadrant, the angle is between 180 ° and 270 °.

We calculate the value of theta as follows

`\begin{gathered} \sin \theta=-(4)/(7) \\ \theta=\sin ^(-1)(-(4)/(7))=-34.85 \\ \text{now, between 180\degree{}and 270\degree} \\ 180+34.85=214.85 \end{gathered}`

Now knowing the angle, we can know the cosine of that angle

`\cos 214.85=-0.82\cong-\frac{\sqrt[]{33}}{7}`