Question

Suppose *u* is a quadrant IV angle with cos(u) = 3/5.

Suppose *v* is a quadrant IV angle with cos(v) = 12/13.

Find the exact value of sin(u-v)


I have gotten to sin120cos150 - sin150cos120 but I am not sure I am correct up to that point and I don't know where to go from there.

Answer 1

draw your triangles in the correct quadrantIs.
Use Pythagoras in each case.

if cosu = 3/5, in IV, then sinu = -4/5
if cosv = 12/13, then sinv = -5/13

sin(u-v)
= sinu cosv - cosu sinv
= (-4/5)(12/13) -(3/5)(-5/13)
= (-48 + 15)/65
= -33/65

Answer 2

437628