# Thread: find the expression

1. ## find the expression

hello for $\displaystyle x \in \mathbb{R}$ find an expression of $\displaystyle Arcsin(sin(x))$ without using trigonometric functions.
(i only need hints )
thanks a lot.

2. Originally Posted by Raoh hello $\displaystyle \forall x \in \mathbb{R}$ find an expression of $\displaystyle Arcsin(sin(x))$ without using trigonometric functions.
(i only need hints )
thanks a lot.
$\displaystyle \arcsin{\sin{x}} = x + 2\pi n, n\in \mathbf{Z}$.

3. ## thanks for your reply,but we only have $\displaystyle \forall x\in \left [ \frac{-\pi}{2},\frac{\pi}{2} \right ],Arcsin(sin(x)) = x$,am i right ? 4. Originally Posted by Raoh thanks for your reply,but we only have $\displaystyle \forall x\in \left [ \frac{-\pi}{2},\frac{\pi}{2} \right ],Arcsin(sin(x)) = x$,am i right ? Yes

5. ## ok,thanks
for $\displaystyle x\in \mathbb{R}$ we have $\displaystyle Arcsin(sin(x)) = x$

6. Raoh, i have plotted its graph, any comments? just double click the graph and it will enlarge for better viewing

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