In this site,The frequency of a trigonometric function is defined as the number of cycles it completes in a given interval.
The formula is : frequency=1/period
The period of a sine function is $2\pi$ [Is it true for all sine function,i.e., basic and general sine function?].
So by formula : frequency=1/$2\pi$.
But, the sine curve completes 1 cycles in the interval $0$ to $2\pi$. So its frequency is $1$.
Why does it conflict with formula?
Where am i doing mistake?
On
You're using 2 (contradicting) definitions of frequency: 1 > "But, the sine curve completes 1 cycles in the interval 0 to 2π. So its frequency is 1." 2 > 1/period
In mathematics, a period of a function $f$ is a real $p$ such that for all $x$, $f(x+p)=f(x)$. You can define frequency as $1/p$ if you wish, but it's not particularly useful.
In physics, a period would typically be an interval of time measured in seconds and the frequency would be its inverse measured in Hertz.
PS: in the definition I labeled "1", you're counting the number of occurrences in one cycle, which can only give 1 by definition, whereas you should be counting the number of occurrences in a fixed interval (e.g. (0,1) )
The problem seems to be the first line, where you state that the frequency is the number of cycles in a given interval. Frequency would better be defined as the number of oscillations per unit time. If the period is $T=2\pi$, than the frequency becomes $\nu=\frac{1}{T}$.
Choosing the frequency as the number of oscillations in a given interval is not a good definition, because the frequency would then depend on your choice of the interval and one function could have multiple frequencies.