Calculus 1

[cedar marten]

Hi, could someone explain to me why we substitute arcsin = t ?

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[deft portal]

arcsin is a function, t is a variable. a function takes a variable as its input, but it's not a variable here

[cedar marten]

aha ok, so we just happen to use t as a function here?

[deft portal]

t is a variable, not a function

[cedar marten]

But why do we bring t in this equation?

why can't we just re-write the function as: 1/ sin x

instead of adding the t in it?

[deft portal]

,,f^{-1}(x) \ne (f(x))^{-1}

[tender bridge]

vin100

[cedar marten]

it's an odd function?

[deft portal]

wdym? you're asking about f?

[cedar marten]

Nvm, your statement reminded me of the definition for even and odd functions

[deft portal]

in general, you can't expect a function's inverse to be equal to its reciprocal

the substitution t = arcsin x is just a relabelling, so that you get your familiar limit ... sin t / t

[cedar marten]

so it's just a relabelling, but it is equivalent to arcsin x?

I think I understood it now, thank you 🙂

[deft portal]

you mean t is arcsin x? ← yes

[cyan pecan]

why? because it works and t is a function, one defines t(x) := arcsin x in a small neighborhood around 0

@cedar marten

[fading violet]

the question was already answered, as reading the channel would tell you

[cedar marten]

+close