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).

Answer 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?