A certain sine function completes 2 full cycles over the interval [0,2π]. Which function rule could model this situation?

The period of the straight sine function y = sin x is 2pi. If not just one but two full cycles appear on the interval [0,2π], then the function becomes

y = sin 2x. As a check, "find" the period of this new function:

Use the formula Period = 2pi/b, where b is the coefficient (2) of 2x in sin 2x.

We get: Period= 2pi/2, or just pi. This is correct; there are two full periods each of length pi.

facundo3141592 facundo3141592 · Answer 2 · 2022-04-05T14:12:34+02:00

The sine function that completes 2 full cycles over the interval [0, 2pi] is:

f(x) = sin(2x).

Which function rule could model this?

We know that the general sine function completes only one full cycle on the interval [0, 2pi].

If we want to have a model that completes two cycles on that interval, then we can compress the parent sine function with a scale factor of 2, this will be:

g(x) = sin(2x)

Whose graph can be seen below, and there you can see that two complete cycles enter on the range [0, 2pi]

If you want to learn more about trigonometric functions, you can read:

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