Question

An object oscillates 4 feet from its minimum height to its maximum height. The object is back at the maximum height every 3 seconds. Which cosine function may be used to model the height of the object?

Answer 1

Answer:

$y=2\text{cos}((\frac{2\pi}{3})t)$

Step-by-step explanation:

We have been given that an object oscillates 4 feet from its minimum height to its maximum height. The object is back at the maximum height every 3 seconds. We are asked to find the cosine function that can be used to model the height of the object.

We know that standard form of cosine function is $y = A\cdot \text{cos}(Bt-C)+D$, where,

|A| = Amplitude,

Period = $\frac{2\pi}{|B|}$,

C = Phase shift,

D = Vertical shift.

Since distance between maximum and minimum is 4, therefore, amplitude will be half of it, that is, $A = 2$.

Since objects gets back to its maximum value in every 3 seconds, therefore, period of the function is 3 seconds. We know that period is given by $\frac{2\pi}{|B|}$, therefore, we can write $\frac{2\pi}{|B|}=3$, therefore, $B = \frac{2\pi}{3}$.

We haven't been given any information about phase and mid-line, we can assume the values of C and D to be zero .

Therefore, our function required function would be $y=2\text{cos}((\frac{2\pi}{3})t)$.