Given that sin x = 4/5, we can use the Pythagorean identity to find the value of cos x.
sin^2 x + cos^2 x = 1(4/5)^2 + cos^2 x = 116/25 + cos^2 x = 1cos^2 x = 9/25cos x = 3/5
Now we can find sin 2x using the double angle identity:
sin 2x = 2sin x cos xsin 2x = 2(4/5)(3/5)sin 2x = 24/25
Therefore, sin 2x = 24/25.
Given that sin x = 4/5, we can use the Pythagorean identity to find the value of cos x.
sin^2 x + cos^2 x = 1
(4/5)^2 + cos^2 x = 1
16/25 + cos^2 x = 1
cos^2 x = 9/25
cos x = 3/5
Now we can find sin 2x using the double angle identity:
sin 2x = 2sin x cos x
sin 2x = 2(4/5)(3/5)
sin 2x = 24/25
Therefore, sin 2x = 24/25.