Finding the fundamental period of −6cos⁡(5πx)I am trying to find the fundamental period of f(x)=−6cos⁡(5πx). I know a periodic function satisfies f(x)=f(x+p).I know that cos⁡(x)'s periodicity is 2π as cos⁡(x+2π)=cos⁡(x) so I just assumed that −6cos⁡(5π⋅1+2π)=−6cos⁡(5π), which it is but apparently this is not correct for the fundamental period?

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Finding the fundamental period of −6cos⁡(5πx)I am trying to find the fundamental period of f(x)=−6cos⁡(5πx). I know a periodic function satisfies f(x)=f(x+p).I know that cos⁡(x)&#039;s periodicity is 2π as cos⁡(x+2π)=cos⁡(x) so I just assumed that −6cos⁡(5π⋅1+2π)=−6cos⁡(5π), which it is but apparently this is not correct for the fundamental period?

caoireoilns · Accepted Answer

Another way of thinking of the periodicity is this: Let f(x)=cos⁡(x). It is easy to show that f(x)=f(x+2πn)  for  n∈N. In addition, f′(x)=f′(x+2πn). Thinking about this problem whilst considering the derivative (rate of change) will show you that the period will involve an additional factor of 5 i.e. cos⁡(5πx) will oscillate more rapidly than cos⁡(x), leading to a smaller period. As a note, the constant out front (−6) will only change the scale of the function, not the period. You can also consider cos⁡(x) has a period of 2π, meaning the length in x required for the cos⁡(x) waveform to complete one &quot;iteration&quot;. With an argument of 5πx, what value (length) of x will make the overall argument 2π? 5πx=2π⇒x=25

Finding the fundamental period of -6\cos(5\pi x) I am trying to find the fundamental perio

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