Inverse functions equations: Why is arcsin(x) = pi an impossible equation?

[Dsas]

Why is arcsin(x) = pi an impossible equation?
sin( arcsin(x) ) = sin(pi) x = sin(pi) = 0.54...

 

[tkhunny]

Why is arcsin(x) = pi an impossible equation?
sin( arcsin(x) ) = sin(pi) x = sin(pi) = 0.54...

1) I cannot tell what it is you are demonstrating. "sin(pi) = 0.54..." doesn't mean anything.
2) Who says arcsin(x) = pi is "impossible"? Besides w/a.
3) sin(pi) = 0 might lead to the obvious conclusion that arcsin(0) = pi
4) Your calculator may not know that pi is a valid result. Normally, on a calculator, you will get arccsin(0) = 0. This has to do with Domain and whether you are talking about an Inverse FUNCTION or an inverse RELATION. Your calculator would typically use (-pi/2,pi/2) and would never give the result arcsin(0) = pi. If you have an Inverse FUNCTION, then, by definition, there is only one result. An inverse relation defined from a periodic function will have infinitely many results.

Okay then, let's answer #2.

 

[sinx]

Why is arcsin(x) = pi an impossible equation?
sin( arcsin(x) ) = sin(pi) x = sin(pi) = 0.54...

sin is always between -1 and +1.
so arcsin(pi) is impossible.

 

[Dr.Peterson]

sin is always between -1 and +1.
so arcsin(pi) is impossible.

But this isn't about arcsin(pi).

The issue is that (unless you are defining arcsin as a multi-valued "function", i.e. a non-function relation), the range of arcsin is defined as [-pi/2,pi/2], so that arcsin(x) can't be pi.

 

[Steven G]

Why is arcsin(x) = pi an impossible equation?
sin( arcsin(x) ) = sin(pi) x = sin(pi) = 0.54...

What on earth does sin(pi) x mean??

The arcsin(x) is an angle (such that sin(angle)=x-little hand waving). An angle can be pi, as in pi radians. So why do you think there is no answer???

 

[pka]

Why is arcsin(x) = pi an impossible equation?

sin is always between -1 and +1. so arcsin(pi) is impossible.

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