PreCalculus
posted by Kimberly on .
Evaluate the expression under the given conditions.? show work please!
sin(AB); tan A=12/5, A in quadrant 3, sinB=3sqrt(10)/10, B in quadrant 4.

Construct 2 triangles,
one in quad III for angle A with sides x=5, y = 12 and r = 13
another in quad IV for angle B with sides x = √10 , y = 3√10 and r = 10
then sinA = 12/13, cosA = 5/13
sinB = 3√10/10 , cosB = √10/10
sin(AB) = sinAcosB  cosAsinB
= (12/13)(√10/10)  (5/13)(3√10/10)
= (12√3  15√10)/130
= 27√10/130