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

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

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Answer 1 · 2018-05-21T16:50:10

i got $\frac{24}{25}$ $24/25$

Explanation:

We have $sin (2 x) = 2 sin (x) cos (x)$ $sin(2x)=2sin(x)cos(x)$ and $cos (x) = \sqrt{1 - {sin}^{2} (x)}$ $cos(x)=sqrt(1-sin^2(x))$
so we get $sin (2 x) = \frac{8}{5} \cdot \sqrt{1 - \frac{16}{25}} = \frac{8}{5} \cdot \frac{3}{5} = \frac{24}{25}$ $sin(2x)=8/5*sqrt(1-16/25)=8/5*3/5=24/25$

Answer 2 · 2018-05-22T04:46:22

$sin 2 x = \pm \frac{24}{25}$ $sin 2x = +- 24/25$

Explanation:

$sin x = \frac{4}{5}$ $sin x = 4/5$ . First, find cos x
${cos}^{2} x = 1 - {sin}^{2} x = 1 - \frac{16}{25} = \frac{9}{25}$ $cos^2 x = 1 - sin^2 x = 1 - 16/25 = 9/25$
$cos x = \pm \frac{3}{5}$ $cos x = +- 3/5$
Since $sin x = \frac{4}{5}$ $sin x = 4/5$ --> x could be in Quadrant 1 or Quadrant 2, therefor, cos x could be positive or negative.
$sin (2 x) = 2 sin x . cos x = 2 (\frac{4}{5}) (\pm \frac{3}{5}) = \pm \frac{24}{25}$ $sin (2x) = 2sin x.cos x = 2(4/5)(+- 3/5) = +- 24/25$
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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If $sin x = \frac{4}{5}$ $\sin x = \frac { 4} { 5]$ , what is $sin 2 x$ $sin 2x$ ?

2 Answers

Explanation:

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