# Math Help - Period of a function

1. ## Period of a function

Just a silly question, got a bit confused. Can a period of a sinusoidal function be the horizontal distance between any two points that enclose a cycle (period)?

The definition, as I've seen, a period of a function is the distance between two sucessive high points or low points on its graph; but in the example they've also shown it as the distance between two points (skipping one) where the graph intercepts the mean line.

2. ## Re: Period of a function

For a regular sinusoidal function the period is the distance between two points that have the same value f(x) and the same slope. You describe it as "skipping one," which is OK, as the point being skipped has opposite slope of the first point. So yes - you can choose successive highs (or lows) - the slope is 0 at both points so it's easy - or you can pick two successive points where f(x)= 0 and slope is equal (i.e. skipping the intervening point where the slope is opposite sign), or you can choose any value for x, note what f(x) and the slope are, then look for the next point with the same value of f(x) and slope.

3. ## Re: Period of a function

Very interesting how the slopes are involved. Indeed, a very precise way to define a period.

Thanks.