Question

Find cosif sin = is in the third quadrant.035OA. -OB.OC. 20OD.Reset Selection-

Answer 1

ANSWER

$A.\text{ }-\frac{4}{5}$

EXPLANATION

We want to find the value of cosθ for:

$\sin\theta=-\frac{3}{5}$

We are given that θ is in the third quadrant. This implies that it is between 180° and 270°.

First, we have to find the value of θ:

$\begin{gathered} θ=\sin^{-1}(-\frac{3}{5}) \\ \\ θ=-36.87\degree\text{ or }216.87\degree \end{gathered}$

Since θ is in the third quadrant, it implies that:

$θ=216.87\degree$

Now, find the value of cosθ:

$\cos(216.87)=-0.8=-\frac{4}{5}$

The answer is option A.