Angle a lies in quadrant 2, and tan(a)= -(12/5). Angle B lies in quadrant 4, and cos(B)= (3/5).

Question

What is the exact value of sin(a+B) ?

Answer 1

tanA = -12/5 = y/x, so in quad II, y = 12, x = -5
r^2 = x^2 + y^2 = 25+144 = 169
r = 13
sinA = 12/13, cosA = -5/13

cos(B)= (3/5) = x/r , where B is in quad IV, so x=3, r=5
x^2 + y^2 = r^2
9 + y^2 = 25
y = -4 ,
sinB = -4/5, cosB = 3/5

sin(A+B) = sinAcosB + cosAsinB
= (12/13)(3/5) + (-5/13)(-4/5)
= .....