## richyw Group Title could someone give me a refresher on what to do with somthing like this $\sin\left( 2\sin^{-1}\left( \frac{1}{2}\right)\right)$ one year ago one year ago

1. Chlorophyll

Start from inside out: 1/2 = sin 30° -> 2arcsin1/2 = 2 * 30 = ... => sin (.. ) = ...

2. richyw

thanks, I made a typo though. I meant to say $\sin\left( 2\sin^{-1}\left( \frac{x}{2}\right)\right)$

3. richyw

$y=\sin\left( 2\sin^{-1}\left( \frac{x}{2}\right)\right)$$\sin^{-1}y=2\sin^{-1}\left(\frac{x}{2}\right)$

4. richyw

nope. super lost!

5. Algebraic!

sin2(theta) = sin(theta)*cos(theta)

6. Chlorophyll

Use the half angle formula: sin2a = 2 sina cosa with a = arcsin (x/2)

7. Algebraic!

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8. Algebraic!

so x/2 * (sqrt(4-x^2))/2

9. richyw

thanks! totally forgot how useful those triangle diagrams are!