If tan(x)=-35/12 and x is in quadrant IV, find the exact values of sin(x/2), cos(x/2), and tan(x/2) without solving for x.
tan(x) = -35/12
sin(x) = -12/37
cos(x) = 35/37
From there, use the half-angle formulas to derive sin(x/2), cos(x/2), and tan(x/2).