Use a half-measure identity to find the indicated function value.

Question

sin t = 24/25 and 1/2π < t < π; find cos 1/2t and cot 1/2t

Answer 1

sint = 24/25

t= 180-73.74 =106.26

t/2= 53.13

cost/2 = cos53.13 = .6

cost = -7/25

90<t<180 t is in quadrant II

divide by 2

45<t/2<90 t/2 is in quadrant I

cost/2 =sqr(1+cost)/2) =sqr((1-7/25)/2) = sqr(18/25)/2) = sqr9/25 = 3/5=.6

sint/2 =sqr(1-cost)/2) = sqr(32/25/2) = sqr(16/26 = 4/5 = .8

cott/2 = cost/2/sint/2 = .6/.8= 3/4