find the fundemental period of f when: f(x)=2cos(3x)
If x is a spatial dimension, that equation would describe the wavelength, not the period.
To find the fundamental period of the function \(f(x) = 2\cos(3x)\), we need to determine the period of the cosine function.
The general form of the cosine function is \(y = A\cos(Bx)\), where \(A\) represents the amplitude and \(B\) determines the frequency of oscillation. The period of the function can be calculated using the formula \(T = \frac{2\pi}{|B|}\).
In the given function, \(f(x) = 2\cos(3x)\), the coefficient in front of \(x\) is 3, which means \(B = 3\). Hence, we can find the period \(T\) as:
\(T = \frac{2\pi}{|3|} = \frac{2\pi}{3}\)
Therefore, the fundamental period of the function \(f(x) = 2\cos(3x)\) is \(\frac{2\pi}{3}\).