could someone give me a refresher on what to do with somthing like this

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

Question

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

anonymous · Answer

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

richyw · Answer

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

richyw · Answer

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

richyw · Answer

nope. super lost!

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

|dw:1354928836731:dw|

anonymous · Answer

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

richyw · Answer

thanks! totally forgot how useful those triangle diagrams are!