SOLUTION: Please help me solve w/work ASAP: If sin(A)=17/45 with pi/2 < A < pi and tan(B)=-105/88 with 3pi/2 < B < 2pi, then what is the exact value of sin(A+B)?

Algebra ->  Trigonometry-basics -> SOLUTION: Please help me solve w/work ASAP: If sin(A)=17/45 with pi/2 < A < pi and tan(B)=-105/88 with 3pi/2 < B < 2pi, then what is the exact value of sin(A+B)?      Log On


   



Question 974495: Please help me solve w/work ASAP: If sin(A)=17/45 with pi/2 < A < pi and tan(B)=-105/88 with 3pi/2 < B < 2pi, then what is the exact value of sin(A+B)?
Answer by Alan3354(69443) About Me  (Show Source):
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Please help me solve w/work ASAP: If sin(A)=17/45 with pi/2 < A < pi and tan(B)=-105/88 with 3pi/2 < B < 2pi, then what is the exact value of sin(A+B)?
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sin(A)=17/45 with pi/2 < A < pi --> Q2
Find the cos(A):
cos%28A%29+=+sqrt%281+-+sin%5E2%28A%29%29
cos%28A%29+=+-sqrt%281736%29%2F45 (Cosine negative in Q2)
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tan(B)=-105/88 with 3pi/2 < B < 2pi --> Q4
Find sine & cosine of B
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tan(B) = y/x
r+=+sqrt%28105%5E2+%2B+88%5E2%29+=+137
sin(B) = y/r = -105/137
cos(B) = x/r = 88/137
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sin(A + B) = sin(A)cos(B) + sin(B)cos(A)
= %2817%2F45%29%2A%2888%2F137%29+%2B+%28-105%2F137%29%2A%28-sqrt%281736%29%2F45%29
= %2817%2A88+%2B+105sqrt%281736%29%29%2F%2845%2A137%29
= %281496+%2B+105sqrt%281736%29%29%2F6165