Question

Given that sin A= -4 over 5 and angle A is in quadrant 3, what is the value of cos(2A)?

Answer 1

Given;

`\sin(A)=-(4)/(5)`

Then, the value of cosine x is;

`\cos(A)=-(3)/(5)`

Because cosine and sine are negative on the third quadrant.

Then;

`\begin{gathered} \cos(2A)=\cos^2(A)-\sin^2(A) \\ \\ \cos(2A)=(-(3)/(5))^2-(-(4)/(5))^2 \\ \\ \cos(2A)=(9)/(25)-(16)/(25) \\ \\ \cos(2A)=-(7)/(25) \end{gathered}`