How do you calculate $sin (arcsin 2 x)$ $sin(arcsin 2x)$ ?

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Answer 1 · 2015-02-08T13:49:34

It will be $2 x$ $2x$

$arcsin 2 x$ $arcsin 2x$ means find the angle of which the sine is $2 x$ $2x$

$sin$ $sin$ means find the sine.
So you first find the angle, and take the sine of it.

So the real question is:
Find the sine of the angle that 'belongs' to a sine of $2 x$ $2x$

In short
$sin$ $sin$ and $arcsin$ $arcsin$ are two opposing operations, they cancel each other out, just like square and square root.

There are limitations, since $sin$ $sin$ must be between $- 1$ $-1$ and $+ 1$ $+1$ ,
so $2 x$ $2x$ is also limited to these boundaries:

$- \frac{1}{2} \leq x \leq + \frac{1}{2}$ $-1/2<=x<=+1/2$

How do you calculate sin(arcsin2x)sin(arcsin 2x)?