If sinA=3/5 when pi/2 < A < pi and cosB=5/13 when 3pi/2 < B < 2pi, find the exact value of the function cos(5pi/6+B).

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  1. Draw your angles in the proper quadrants.
    Recall again that
    sinθ = y/r
    cosθ = x/r
    Given the points for A and B, and recall your basic Pythagorean triples,
    sinA = 3/5
    cosA = -4/5
    sinB = -12/13
    cosB = 5/13

    cos(5π/6 + B) = cos(5π/6) cosB - sin(5π/6) sinB
    Now just plug and chug. Did angle A get lost?

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