Question

Given sin thata = 2/5 and 0° < thata < 90°. find sin 2 thata​

Answer 1

Recall the double angle identity:

$\sin2\theta=2\sin\theta\cos\theta$

With $\theta$ measuring between 0º and 90º, we know $\cos\theta>0$. So from the Pythagorean identity, we get

$\sin^2\theta+\cos^2\theta=1\implies\cos\theta=\sqrt{1-\sin^2\theta}=\dfrac{\sqrt{21}}5$

Then

$\sin2\theta=2\dfrac25\dfrac{\sqrt{21}}5=\dfrac{4\sqrt{21}}{25}$