Question

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

Answer 1

ANSWER:

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

STEP-BY-STEP EXPLANATION:

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

We calculate the value of theta as follows

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

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

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