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

2 Answers
Sonnhard
May 21, 2018

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#

Nghi N
May 22, 2018

#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.

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