Question 965062
evaluate the expression given that sina=-4/5with pi<a<3pi/2 and cos b=5/13 with 0<b<pi/2
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sina=-4/5 (Q3)
cosa=-3/5
cosb=5/13 (Q1)
sinb=12/13
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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
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Check:
sina=-4.5
a=233.13&#730;
cosb=5/13
b=67.38&#730;
a-b=165.75&#730;
a+b=300.51&#730;
cos(a-b)=cos(165.75)&#8776;-0.9692
exact value as computed above=-63/65&#8776;-0.9692
sin(a+b)=sin(300.51)&#8776;-0.8615
exact value as computed above=-56/65&#8776;-0.8615