SOLUTION: find exact value of a) sin(alpha+beta); b) cos(alpha+beta); c) tan(alpha-beta) given that cos(alpha)=radical 5/5 5 in Q1 & sin(beta)= -4/5 in Q4

Algebra ->  Trigonometry-basics -> SOLUTION: find exact value of a) sin(alpha+beta); b) cos(alpha+beta); c) tan(alpha-beta) given that cos(alpha)=radical 5/5 5 in Q1 & sin(beta)= -4/5 in Q4      Log On


   

Question 960793: find exact value of a) sin(alpha+beta); b) cos(alpha+beta); c) tan(alpha-beta) given that cos(alpha)=radical 5/5 5 in Q1 & sin(beta)= -4/5 in Q4
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
find exact value of
a) sin(alpha+beta)
b) cos(alpha+beta)
c) tan(alpha-beta)
given that cos(alpha)=sqrt(5)/5 in Q1 & sin(beta)= -4/5 in Q4
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If cos(a) = sqrt(5)/5 , sin(a) = sqrt(5^2-5)/5 = sqrt(20)/5 = (2sqrt(5)/5
Then tan(a) = sin(a)/cos(a) = [2sqrt(5)/5]/[sqrt(5)/5] = 2
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If sin(b) = -4/5 in QIV, cos(b) = sqrt(5^2-4^2)/5 = 3/5
Then tan(b) = sin(b)/cos(b) = (-4/5)/(3/5) = -4/3
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a) sin(a+b)=sin(a)cos(b)+cos(a)sin(b)=(2sqrt(5)/5)*(3/5)+(sqrt(5)/5)*(-4/5)
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= (6sqrt(5)/25)-4sqrt(5)/25 = 2sqrt(5)/25
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Comment:: For b) and c) fill in the values to get the answers::
b) cos(a+b) = cos(a)cos(b)-sin(a)sin(b)
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c) tan(a-b) = [tan(a)-tan(b)]/[1+tan(a)*tan(b)]
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Cheers,
Stan H.