Question

If `\sin x = \frac { 4} { 5]`, what is `sin 2x`?

Answer 1

i got `24/25`

Explanation:

We have `sin(2x)=2sin(x)cos(x)` and `cos(x)=sqrt(1-sin^2(x))`
so we get `sin(2x)=8/5*sqrt(1-16/25)=8/5*3/5=24/25`

Answer 2

`sin 2x = +- 24/25`

Explanation:

`sin x = 4/5`. First, find cos x
`cos^2 x = 1 - sin^2 x = 1 - 16/25 = 9/25`
`cos x = +- 3/5`
Since `sin x = 4/5` --> x could be in Quadrant 1 or Quadrant 2, therefor, cos x could be positive or negative.
`sin (2x) = 2sin x.cos x = 2(4/5)(+- 3/5) = +- 24/25`
If x lies in Q. 1 --> 2x lies in Q. 2 --> sin 2x is positive
If x lies in Q. 2 --> 2x lies in Q. 3 --> sin 2x is negative.