Thread: Are these trigonometric functions even or odd?

x(t) = 20cos(2π*40t-0.4π)

x(t) = exp(-8πt)

x[n] = exp(cos(2πn/5))

x[n] = u[n] + u[-n]

x[n] = u[n] - u[-n] + 5δ[n]

Many thanks in advance.

Originally Posted by essedra

x(t) = 20cos(2π*40t-0.4π)

x(t) = exp(-8πt)

x[n] = exp(cos(2πn/5))

x[n] = u[n] + u[-n]

x[n] = u[n] - u[-n] + 5δ[n]

Many thanks in advance.

f(-x) = f(x) ... even

f(-x) = -f(x) ... odd

now what?

Originally Posted by skeeter

f(-x) = f(x) ... even

f(-x) = -f(x) ... odd

now what?

Yes, I know, but how can I apply this and see the result?

I mean to decompose them into even & odd parts?

x(t) = 20cos(2π*40t-0.4π)

final result ... x(-t) is not equal to x(t) or -x(t) ... x(t) is neither even or odd

Originally Posted by essedra

Yes, I know, but how can I apply this and see the result?

Sometimes one must just have some prior information.
The function is even and is odd.
On the other hand, you should be able to prove that is even.

Can you show that is neither even nor odd?

Originally Posted by Plato

Sometimes one must just have some prior information.
The function is even and is odd.
On the other hand, you should be able to prove that is even.

Can you show that is neither even nor odd?

I can interprete it from the graph of the function, that it's not even nor odd, but I don't know how to prove it...

Originally Posted by essedra

I can interprete it from the graph of the function, that it's not even nor odd, but I don't know how to prove it...

For all :

Is is possible that

Is is possible that

If the answer to both is no, then it is neither even nor odd.

Oh, I see now. It's simple as cake. Thank you...