Behaviour of simple cos function

Question

I have a function:

$\cos(4*\pi/10*x)*\cos(2*\pi*f*t)$

where:

'$x$' represents x-axis; '$f$' is the frequency which remains constant, and'$t$' is a time vector.

As I keep changing the time instant manually, and plot the function in 2D, I observe that the plot does not change once the value of '$f*t$' exceeds $1$. The plot changes only when value of '$f*t$' ranges from $0.1$ to $1$.

I am curious why that happens? I am using the website fooplot online plotter.

Answer 1

What do you mean exactly when you say that the function "does not change"? Also, showing your plots would be helpful. I mean, since it's an oscillatory function it'll always repeat itself after every full period, which is written as $f*t=n$, with $n$ any natural number.

Answer 2

The cosine is a periodic function with period $2\pi$, meaning that for all $x$ it holds that $$\cos(x+2\pi)=\cos(x)$$