Evaluate sin(pi/3 - a) if cos(a) = -0.6 and pi < a < 3pi/2

Answer 1

Answer 2

cosa = -.6 = -3/5, a is in quadrant 3

a = 360- cos^-1(-.6) = 233.13 degrees = about 1.295pi

sin(60-233.13) = sin(-173.13)= about -0.12

sin(pi/3 -1.295pi) = about sin(-.962pi) = sin-173.1303 = about -.1196 = about -0.12

=-12/100=-3/50

or

sina = -.8=-4/5 (sqr(25-9)=sqr16=4 and 4/5 =.8)

use difference formula (sin(x-y) = sinxcosy-cosxsiny)

sin(pi/3-a) =sin(pi/3)cos(a)- cos(pi/3)sin(a)

= (sqr3/2)(-3/5)-(1/2)(-4/5)

= -3sqr3/10 +4/10

= (4-3sqr3/10)/10

=about -0.1196