# find the expression

• Jul 10th 2009, 09:54 AM
Raoh
find the expression
hello(Happy)
for $\displaystyle x \in \mathbb{R}$ find an expression of $\displaystyle Arcsin(sin(x))$ without using trigonometric functions.
(i only need hints(Wink) )
thanks a lot.
• Jul 10th 2009, 09:58 AM
Prove It
Quote:

Originally Posted by Raoh
hello(Happy)
$\displaystyle \forall x \in \mathbb{R}$ find an expression of $\displaystyle Arcsin(sin(x))$ without using trigonometric functions.
(i only need hints(Wink) )
thanks a lot.

$\displaystyle \arcsin{\sin{x}} = x + 2\pi n, n\in \mathbf{Z}$.
• Jul 10th 2009, 10:34 AM
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 ?(Thinking)
• Jul 10th 2009, 11:02 AM
Prove It
Quote:

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 ?(Thinking)

Yes
• Jul 10th 2009, 11:11 AM
Raoh
ok,thanks
for $\displaystyle x\in \mathbb{R}$ we have $\displaystyle Arcsin(sin(x)) = x$
• Aug 12th 2009, 02:27 AM
pacman
Raoh, i have plotted its graph, any comments? just double click the graph and it will enlarge for better viewing