Assume that A and B are in standard position and that sin A = 1/2, cos A 0, tan B = 3/4, and sinB

Question

Assume that A and B are in standard position and that sin A = 1/2, cos A >0, tan B = 3/4, and sinB<0

Cos (A-B)

Reiny · Accepted Answer

from sin A = 1/2, cos A >0, we know that A has to be in quadrant I, so cosA = √3/2
from tan B = 3/4, and sinB<0, we know that B must be in quadrante III, so sinB=-3/5 and cosB = -4/5

Cos(A-B) = cosAcosB + sinAsinB
= √3/2(-4/5) + 1/2(-3/5)
= (-4√3 - 3)/10