Can Trig Functions Satisfy These Conditions for Even and Odd Numbers?

[mohamadh95]

is there any function h(x) that satisfies these conditions:
h(x)=0 when x is even
h(x)=1 when x is odd
and is there there any function g(x) such that:
g(x)=0 when x is odd
g(x)=1 when x is even
thank you.

 

[vanhees71]

What's the desired domain? If it's only $\mathbb{Z}$ think about the expression $(-1)^x$!

 

[mohamadh95]

What's the desired domain? If it's only $\mathbb{Z}$ think about the expression $(-1)^x$!

Thank you for your quick reply g(x) can be (1+(-1)^x)/2 and h(x) (1-(-1)^x)/2

 

[D H]

The trig functions are quite nice if the domain is ℝ. For example, look at cos²(pi*x) or cos(2*pi*x).