Question

Find sin 2x if cos x=-2/3 and x is in quadrant 2

Answer 1

-4√5/9.

Explanation:

if cos x = -2/3 then sin x = √(1 - (-2/3)^2)

= √(5/9)

= √5/3.

(As x is in quadrant 2 sin x is positive).

So:

sin2x = 2 sin x cos x

= 2 * √5/3 * -2/3

= -4/3 * √5/3

= -4√5/9.