If \sin x = \frac { 4} { 5]sinx=45, what is sin 2xsin2x?

2 Answers
May 21, 2018

i got 24/252425

Explanation:

We have sin(2x)=2sin(x)cos(x)sin(2x)=2sin(x)cos(x) and cos(x)=sqrt(1-sin^2(x))cos(x)=1sin2(x)
so we get sin(2x)=8/5*sqrt(1-16/25)=8/5*3/5=24/25sin(2x)=8511625=8535=2425

May 22, 2018

sin 2x = +- 24/25sin2x=±2425

Explanation:

sin x = 4/5sinx=45. First, find cos x
cos^2 x = 1 - sin^2 x = 1 - 16/25 = 9/25cos2x=1sin2x=11625=925
cos x = +- 3/5cosx=±35
Since sin x = 4/5sinx=45 --> 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) = +- 24/25sin(2x)=2sinx.cosx=2(45)(±35)=±2425
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.