Nested trigonometric functions: sine and cosine

 
 

\sin \, ( \, \cos (x) \, )   and   \cos \, ( \, \sin (x) \, )

Why is   \cos \, ( \, \sin (x) \, )   always greater?

\cos \, ( \, \sin (x) \, ) \; > \; \sin \, ( \, \cos (x) \, )

 
And,
 

A(x) \; = \; \cos \,( \,\sin \,( \,\cos \,(......(\sin \,(x))))...)))
B(x) \; = \; \sin \,( \,\cos \,( \,\sin \,(......(\cos \,(x))))...)))

 
Does the ratio   A(x) \, / \, B(x)   depend on   x ?

 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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