Question

I have tried and tried to understand double angle identities but it just won't stick.


if sin x = -0.6 and 180 (degrees) < x < 270 (degrees), find the exact value of sin 2x

Answer 1

sin 2x = 2 sin x cos x
x is in quadrant 3 so cos x is negative
sin 2x = 2(-0.6) cos x
but
cos^2 x = 1 - sin^2 x
cos^2x = 1 - .36 = .64 = 64 * 10^-2
so
cos x = + or - 8*10^-1 = -0.8 because we know it is -
so
sin 2x = 2 (-0.6)(-0.8) = + 0.96