How do you determine if #F(x)= cos (sin x)# is an even or odd function?

1 Answer

A function #g# is said to be even, provided that #g(–x) = g(x)#, for all x.

A function #f# is said to be odd, provided that #f(–x) = –f(x)#, for all x.

Now we have that

#F(-x)=cos(sin(-x))=cos(-sinx)=cos(sinx)=F(x)# hence #F# is even.

Such functions have graphs that are symmetric about the y-axis as can be seen in the graph below

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