SOLUTION: please please help :define a function f:[0,2pi]->real number such that f(0)=f(2pi).show that there exist an element x in [0,pi] such that f(x)=f(x+pi). thanks a lot.

Algebra ->  Functions -> SOLUTION: please please help :define a function f:[0,2pi]->real number such that f(0)=f(2pi).show that there exist an element x in [0,pi] such that f(x)=f(x+pi). thanks a lot.      Log On


   

Question 811967: please please help :define a function f:[0,2pi]->real number such that f(0)=f(2pi).show that there exist an element x in [0,pi] such that f(x)=f(x+pi). thanks a lot.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Define

Let



and



Show

Let

Then

Interestingly enough, the above result notwithstanding:



John

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