Question

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

Answer 1

C

Explanation:

Edge2021

Answer 2

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=√(1-\sin^2\theta)=\frac{√(21)}5`

Then

`\sin2\theta=2\frac25\frac{√(21)}5=(4√(21))/(25)`