# Math Help - what is inverse sine of sin3 equal to?

1. ## what is inverse sine of sin3 equal to?

Hi,

$\sin^{-1}(sin3)$. Find the exact value.

what is that equal to in exact value?

it's not equal to 3 because the inverse sine function has a range of -pi/2 << y << pi/2.

I graphed the inverse sine on mathematica and it gave me a value of 0.559 etc but I don't know how to find the exact value of this

Thanks

2. acctually in general in the equation $

\sin^{-1}(sin3)
$

both the sin's will give no effect because finding sin3 and inversing it again with sin give 3 itself

Let the expression be equal to x, x being angle.
$
sin^-1(sin(3))=x
$

$
sin(x)=sin(3)
$

$
x=3
$

4. Originally Posted by differentiate
Hi,

$\sin^{-1}(sin3)$. Find the exact value.

what is that equal to in exact value?

it's not equal to 3 because the inverse sine function has a range of -pi/2 << y << pi/2. ... correct

I graphed the inverse sine on mathematica and it gave me a value of 0.559 etc but I don't know how to find the exact value of this

Thanks
note that an angle of measure 3 radians is in quad II.

$\sin(3) = \sin(\pi-3)$ , where $\pi-3$ is a quad I angle

$\arcsin[\sin(\pi-3)] = \pi-3$

5. Originally Posted by baqijan
Let the expression be equal to x, x being angle.
$
sin^-1(sin(3))=x
$

$
sin(x)=sin(3)
$

$
x=3
$
Go back and read the original post. 3 is not between $-\pi/2$ and $\pi/2$ $sin^{-1}(sin(x))= x$ is only true for x in that range.