Consider this example provided by my teacher:

5. Given cosa = - and cos B = -, a and B in quadrant III, find (a) sin(a + B), (b) tan(a + B), and (c) the quadrant of a + B. 17 15 5 4 B' 8 3 sina = - sinB = = 8 COST - cosp = - 17 tana = 15 tanB = = W/A CO (a) sin(A + B) = sinAcosB + cosAsinB = (-15)(-3) +(-3)(-3) =35+ 32 77 85 4 tanA+tanB 24 45+32 77 77 (b) tan(A + B) = = 1-tanAtanB -36 36 24 24 24-60 15 15 3 4 8 15 32 77 24 77 OR 8 3 38 . 36 - X 1- 15 4 1- 60 24 36 36 74 24 24 24 S A X X X (c ) Quadrant II T X C5. Given sina = - 25 and sin B = =, a and B in quadrant II, find (a) sin(a + B), (b) tan(a + B), and (c) the quadrant of a + B