SOLUTION: evaluate the expression given that sina=-4/5with pi<a<3pi/2 and cos b=5/13 with 0<b<pi/2 1. cos(a-b) 2.sin(a+b)

Algebra ->  Trigonometry-basics -> SOLUTION: evaluate the expression given that sina=-4/5with pi<a<3pi/2 and cos b=5/13 with 0<b<pi/2 1. cos(a-b) 2.sin(a+b)       Log On


   

Question 965062: evaluate the expression given that sina=-4/5with pi 1. cos(a-b)
2.sin(a+b)

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
evaluate the expression given that sina=-4/5with pi ***
sina=-4/5 (Q3)
cosa=-3/5
cosb=5/13 (Q1)
sinb=12/13
..
1. cos(a-b)=cosa*cosb+sina*sinb=-3/5*5/13+-4/5*12/13=-15/65-48/65=-63/65
2.sin(a+b)=sina*cosb+cosa*sinb=-4/5*5/13+-3/5*12/13=-20/65-36/65=-56/65
..
Check:
sina=-4.5
a=233.13˚
cosb=5/13
b=67.38˚
a-b=165.75˚
a+b=300.51˚
cos(a-b)=cos(165.75)≈-0.9692
exact value as computed above=-63/65≈-0.9692
sin(a+b)=sin(300.51)≈-0.8615
exact value as computed above=-56/65≈-0.8615