Asymptotic expansions of the sine function

[Robin04]

Homework Statement

$\sin{(a + b)}\sim f_1(a)+f_2(b)$

Relevant Equations

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There are no restrictions for $a,b,f_1,f_2$. One solution is the first order Taylor series expansion of course with $f_1(a)=a,f_2(b)=b$, but are there any other solutions? I tried the Bhaskara formula but I couldn't express it in this form.

 

[pasmith]

Asymptotic in what limit?

 

[Robin04]

Asymptotic in what limit?

Depends on the expansion, it's not specified at this point yet.