# Thread: Are these trigonometric functions even or odd?

1. ## 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]

2. ## Re: Are these trigonometric functions even or odd?

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]

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

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

now what?

3. ## Re: Are these trigonometric functions even or odd?

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?

4. ## Re: Are these trigonometric functions even or odd?

x(t) = 20cos(2π*40t-0.4π)
$\displaystyle x(t) = 20\cos(80\pi t - 0.4\pi)$

$\displaystyle x(-t) = 20 \cos(-80\pi t - 0.4\pi) = 20\cos[-(80\pi t + 0.4\pi)] = 20 \cos(80\pi t + 0.4\pi)$

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

5. ## Re: Are these trigonometric functions 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 $\displaystyle \cos(x)$ is even and $\displaystyle \sin(x)$ is odd.
On the other hand, you should be able to prove that $\displaystyle f(x)=|x|$ is even.

Can you show that $\displaystyle f(x)=e^x$ is neither even nor odd?

6. ## Re: Are these trigonometric functions even or odd?

Originally Posted by Plato
Sometimes one must just have some prior information.
The function $\displaystyle \cos(x)$ is even and $\displaystyle \sin(x)$ is odd.
On the other hand, you should be able to prove that $\displaystyle f(x)=|x|$ is even.

Can you show that $\displaystyle f(x)=e^x$ 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...

7. ## Re: Are these trigonometric functions even or odd?

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 $\displaystyle x$:

Is is possible that $\displaystyle e^x=e^{-x}~?$

Is is possible that $\displaystyle -e^x=e^{-x}~?$

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

8. ## Re: Are these trigonometric functions even or odd?

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