Quandaries
and Queries 

My name is Kate and I'm a student in high school (1012). Please help me verify the identity: Also I am having trouble withdetermining whether
f(x) is odd, even, or neither 

Hi Kate, What I see here is the trig identity
and hence
Thus
Can you complete it now? In the second problem I would experiment a little. If f(x) is even then for any number x,
Choose some numbers x and try.
Thus f(x) is not even because f(2) is not equal to f(2). But f(2) = f(2) and the requirement that f(x) be odd is that for all numbers x, f(x) = f(x). Is that true, if f(x) = x^{3}  x is f(x) = f(x)? Can you prove it? Penny 

