SOLUTION: Given that sin(alpha)=2/3 and sin(beta)=-1/3 with alpha in Quadrant 2 and beta in quadrant 4, find sin(alpha+beta) and tan(alpha+beta)

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Question 613689: Given that sin(alpha)=2/3 and sin(beta)=-1/3 with alpha in Quadrant 2 and beta in quadrant 4, find sin(alpha+beta) and tan(alpha+beta)
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Given that sin(alpha)=2/3 and sin(beta)=-1/3 with alpha in Quadrant 2 and beta in quadrant 4, find sin(alpha+beta) and tan(alpha+beta)
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use x for alpha and y for beta
sinx=2/3 (quad II)
cosx=-√5/3
tanx=-2/√5
..
siny=-1/3 (quad IV)
cosy=√8/3
tany=-1/√8
..
Using sin and tan addition formulas:
sin(x+y)
=sinxcosy+cosxsiny
=2/3*√8/3+(-√5/3)(-1/3)
=2√8/9+√5/9
=(2√8+√5)/9
≈.88
..
tan(x+y)=(tanx+tany)/(1-tanxtany)
=(-2/√5-1/√8)/(1-(-2/√5*-1/√8))
≈-1.25/.683
≈-1.83
..
ans:
sin(alpha+beta)≈.88
tan(alpha+beta)≈1.83