use the given information to find each value

Question

A) cos 2t B) sin 2t C)cos (t/2) D)sin (t/2) Cos t =3/5, where 0 < t < pi/2 Sin t = -3/5,where pi < t < 3pi/2

Answer 1

use the double and half angle formulas

cos2t= 2cos^2(t) -1, cos(t/2) = + or - sqr((1+cost/2)

sin(t/2) = + or - sqr((1-cost)/2)

for cost = 3/5 in Quadrant I

cos2t+ 2(3/5)^2 - 1 = 18/25-1= -7/25

cos(t/2) = + or - sqr(1+3/5)/2) = + or - 2/sqr5

sin2t = 2sintcost = 2(4/5)(3/5) = 24/25

sin(t/2) + + or - sqr((1-cost)/2) = + or - 1/sqr5

for sint=-3/5, cost=4/5 in quadrant III

sin2t = 2sintcost = 2(3/5)(-4/5) = -24/25

sin(t/2) = + or - sqr((1+cost)/2) = + or - 1/sqr10

cos(t/2) = + or - sqr((1-cost)/2) = + or - 3/sqr10

cos2t =2(4/5)^2 - 1 = 32/25-1 = 7/25