How to simplify an iterated trigonometric expression

[Leo Liu]

Homework Statement

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Relevant Equations

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eg $\cos (\sin x)$
Asking this question out of curiosity.

 

[Mark44]

Homework Statement:: .
Relevant Equations:: .

eg $\cos (\sin x)$
Asking this question out of curiosity.

I don't see how you're going to be able to get anything simpler than that.

 

[FactChecker]

Typically this can only be done with the partial sums of the Taylor series of the functions. There are a variety of ways to calculate a partial sum of the composition, including matrix multiplication.

 

[Delta2]

If you are interested about the Fourier series of cos(cos x) or cos (sin x) I think they are related to the Bessel functions.

 

[Leo Liu]

If you are interested about the Fourier series of cos(cos x) or cos (sin x) I think they are related to the Bessel functions.

Thank you this is the best answer I got :D

 

[WWGD]

Or maybe you want something like :

$Cos^2(sinx)+ Sin^2(sinx)=1$

So that $Cos(sinx)=\sqrt {1-Sin^2(sinx)}$?

 

[Mark44]

Or maybe you want something like :

$Cos^2(sinx)+ Sin^2(sinx)=1$

So that $Cos(sinx)=\sqrt {1-Sin^2(sinx)}$?

I thought of something like this, as well as a Taylor or Maclaurin series, but none of these seemed like they would serve to simplify the given expression.