SOLUTION: if cos(a) is 2/3 and sin(b) is 4/5 what is cos(a+b)

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Question 690398: if cos(a) is 2/3 and sin(b) is 4/5 what is cos(a+b)
Answer by lwsshak3(11628) About Me  (Show Source):
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if cos(a) is 2/3 and sin(b) is 4/5 what is cos(a+b)
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cos a=2/3=adj side/hypotenuse
opp side=√(3^2-2^2)=√(9-4)=√5
sin a=√5/3
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sin b=4/5 (3-4-5 right triangle)
cos b=3/5
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cos(a+b)=cos a cos b -sin a sin b
=2/3*3/5 -√5/3*4/5
=6/15-4√5/15
=(6-4√5)/15
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calculator check:
a=cos^1(2/3)≈.8411
b=sin^-1(4/5)=.9273
cos(a+b)=cos(1.7684)=-0.1962..
(6-4√5)/15=-0.1962..