SOLUTION: if tan theta=5/4 find the value of 3 sin theta + 4 cos theta/3 sin theta - 4cos

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Question 962265: if tan theta=5/4 find the value of 3 sin theta + 4 cos theta/3 sin theta - 4cos

Answer by Alan3354(69443) About Me  (Show Source):
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if tan theta=5/4 find the value of 3 sin theta + 4 cos theta/3 sin theta - 4cos
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tangent = y/x
r+=+sqrt%28y%5E2+%2B+x%5E2%29+=+sqrt%2841%29
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sin = y/r = 5/sqrt(41) = 5sqrt(41)/41
cos = x/r = 4sqrt(41)/41
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(3sin + 4cos)/(3sin - 4cos) = ((15sqrt(41)+16sqrt(41))/((15sqrt(41)-16sqrt(41))
= -31