Question

If sinA = 4/5 with A in Q2, and sinB = -3/5 with B in Q4, find cos(A - B)

Answer 1

Angle A is in the second quadrant, hence cosA will be negative.

`\begin{gathered} \cos A=-\sqrt[]{1-\sin ^2A} \\ =-\sqrt[]{1-((4)/(5))^2} \\ =(-3)/(5) \end{gathered}`

Angle B is in the 4th quadrant, hence cosB will be positive,

`\begin{gathered} \cos B=\sqrt[]{1-\sin ^2B} \\ =\sqrt[]{1-((-3)/(5))^2} \\ =(4)/(5) \end{gathered}`

Cos(A-B) can be determined as,

`\begin{gathered} \cos (A-B)=\cos A\cos B+\sin A\sin B \\ =((-3)/(5))*(4)/(5)+(4)/(5)*((-3)/(5)) \\ =(-12)/(25)-(12)/(25) \\ =(-24)/(25) \end{gathered}`

Thus, option (a) is the correct solution.