graph$$\sin (y) =\sin (x)$$

Question

anonymous · Answer

Well, that's gonna look awesome. Take the arcsin on both sides, and you get,

y = arcsin(sin(x))

Are you supposed to graph this by hand or how?

anonymous · Answer

they undo each other, dont they. the arcsin and sin

hartnn · Answer

|dw:1348749590274:dw|

anonymous · Answer

Yeah you need to make sure you dont screw up at pi, 2pi, and so on.

unklerhaukus · Answer

are there more solution curves

anonymous · Answer

isnt it just y=x as the 2 functions cancel out.

anonymous · Answer

Here's a relation between sin, arcsin(sin(x)) and x

hartnn · Answer

whats the max amplitude and how do we get it analytically ?

hartnn · Answer

pi/2 ?

unklerhaukus · Answer

$\arcsin n$  returns one value for many values of $n$

hartnn · Answer

yes,cos its periodic with period 2pi

anonymous · Answer

CAN SOMEONE EXPLAIN ME WHY IT IS NOT SAME AS y=x

hartnn · Answer

in the range pi/2 to 3pi/2, sin is negative

anonymous · Answer

Take the dev of sin(x), which is cos(x), and for every zero of cos, you have the max and min of sin.

ash2326 · Answer

@heedcom we are tempted to just cancel and simplify it as y=x
but this is not that simple
cause the range of arc sin is $\large\frac{-\pi}{2}, \frac{\pi}{2}$
if x is in this range we'd get y=x
but supposedly x=pi
$$y=\arcsin(\sin \pi)$$
$$y=\arcsin(0)=0\ne \pi$$
@sauravshakya

hartnn · Answer

so it will be y=-x in the range pi/2 to 3pi/2
got this @sauravshakya

anonymous · Answer

You see the Forward Function is NOT 1:1 - so the Inverse function , strictly speaking does NOT Exist @sauravshakya

unklerhaukus · Answer

i never said it was a function

ash2326 · Answer

$$y=\sin (\arcsin x)=x$$
this is always true

anonymous · Answer

It is like the equation
$$   x^2 = y^2$$

unklerhaukus · Answer

can you graph the solutions Mikael ?

anonymous · Answer

OH...... got it. THANX @ash2326

hartnn · Answer

are my and @gezimbasha graphs correct ?

anonymous · Answer

sure, thanks

anonymous · Answer

Yes @UnkleRhaukus |dw:1348750437001:dw|

anonymous · Answer

Here you go, the green one is cos(x). You can see there's stops at every pi/2 and 3pi/2, those are cos(x) zeros.

unklerhaukus · Answer

the graphs so far are only part of the solution set

anonymous · Answer

For the problem discussed here the graphs are separate points with periodic repetition|dw:1348750632971:dw|