Question

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

Answer 1

From the question we have that

`\begin{gathered} sinA=-(4)/(5) \\ in\text{ quadrant 3} \end{gathered}`

We wan to find cos A.

We have

`\begin{gathered} sinA=-(4)/(5)=(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=√(9) \\ adj=3 \end{gathered}`

And we have

`cosA=(adj)/(hyp)=(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=-(3)/(5)`