Question

Given that sin A= -4 over 5,and angle A is in quadrant 3, what is the value of cos A?

Answer 1

SOLUTION

From the question we have that

$\begin{gathered} sinA=-\frac{4}{5} \\ in\text{ quadrant 3} \end{gathered}$

We wan to find cos A.

We have

$\begin{gathered} sinA=-\frac{4}{5}=\frac{opp}{hyp} \\ From\text{ Pythagoras } \\ hyp^2=opp^2+adj^2 \\ 5^2=4^2+adj^2 \\ adj^2=25-16 \\ adj^2=9 \\ adj=\sqrt{9} \\ adj=3 \end{gathered}$

And we have

$cosA=\frac{adj}{hyp}=\frac{3}{5}$

Now since cos theta is negative in the 3rd quadrant and angle A is in the third quadrant, then

The answer is

$cosA=-\frac{3}{5}$