sin( 2A ) = 2 sin( A ) cos( A )
We can find sin( A ) using the Pythagorean identity.
sin2 A + cos2 A = 1
sin2 A + (-4/5)2 = 1
sin2 A + (16/25) = 1
sin2 A = 1 - 16/25
sin2 A = 9/25 Take the square root of both sides.
sin A = 3/5 Since sin is positive in Quadrant II, we only take the positive root.
Now we can find sin( 2A ) using the double-angle identity.
sin( 2A ) = 2 sin( A ) cos( A )
sin( 2A ) = 2 (3/5) (-4/5)
sin( 2A ) = -24/25
sin( 2A ) = 2 sin( A ) cos( A )
We can find sin( A ) using the Pythagorean identity.
sin2 A + cos2 A = 1
sin2 A + (-4/5)2 = 1
sin2 A + (16/25) = 1
sin2 A = 1 - 16/25
sin2 A = 9/25 Take the square root of both sides.
sin A = 3/5 Since sin is positive in Quadrant II, we only take the positive root.
Now we can find sin( 2A ) using the double-angle identity.
sin( 2A ) = 2 sin( A ) cos( A )
sin( 2A ) = 2 (3/5) (-4/5)
sin( 2A ) = -24/25