Find the EXACT value of cos(A+B) if sin A = −5/13 where A is in Quadrant IV and sin B = −8/17 where B is in Quadrant III. Assume all angles are measured from standard position. cos(A+B) =
First, use the pythagorean theorem to find cosA and cosB:
A: the adjacent side is ±√( 13^2 - 5^2 ) = ±12. Since A is in quadrant IV, it's +12. So cosA = 12/13.
B: adjacent is ±√( 17^2 - 8^2 ) = ±15. Since B is in quadrant III, it's -15, so cosB = -15/17
Next, use this sum identity:
cos(A+B) = cosA*cosB - sinA*sinB
Plug in the numbers and solve......