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Denis Serre
Denis Serre
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The convention that $\sin^2 x = (\sin x)^2$, while in general $f^2(x) = f(f(x))$, is often called illogical, but it does not lead to conflicts because nobody uses $\sin(\sin x))$$\sin(\sin x)$.

But is this really true? Or is there a real-world application in which $\sin(\sin x))$$\sin(\sin x)$ occurs? Or maybe something a bit more general, like $\sin(C \sin x)$ for some constant $C \neq 0$?

The convention that $\sin^2 x = (\sin x)^2$, while in general $f^2(x) = f(f(x))$, is often called illogical, but it does not lead to conflicts because nobody uses $\sin(\sin x))$.

But is this really true? Or is there a real-world application in which $\sin(\sin x))$ occurs? Or maybe something a bit more general, like $\sin(C \sin x)$ for some constant $C \neq 0$?

The convention that $\sin^2 x = (\sin x)^2$, while in general $f^2(x) = f(f(x))$, is often called illogical, but it does not lead to conflicts because nobody uses $\sin(\sin x)$.

But is this really true? Or is there a real-world application in which $\sin(\sin x)$ occurs? Or maybe something a bit more general, like $\sin(C \sin x)$ for some constant $C \neq 0$?

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user22882
user22882

Is there any use for $\sin(\sin x)$?

The convention that $\sin^2 x = (\sin x)^2$, while in general $f^2(x) = f(f(x))$, is often called illogical, but it does not lead to conflicts because nobody uses $\sin(\sin x))$.

But is this really true? Or is there a real-world application in which $\sin(\sin x))$ occurs? Or maybe something a bit more general, like $\sin(C \sin x)$ for some constant $C \neq 0$?