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)?
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sin(A)=17/45 with pi/2 < A < pi --> Q2
Find the cos(A):
{{{cos(A) = sqrt(1 - sin^2(A))}}}
{{{cos(A) = -sqrt(1736)/45}}}  (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(105^2 + 88^2) = 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)
= {{{(17/45)*(88/137) + (-105/137)*(-sqrt(1736)/45)}}}
= {{{(17*88 + 105sqrt(1736))/(45*137)}}}
= {{{(1496 + 105sqrt(1736))/6165}}}