the period of a function is 4π. how many cycles of the function occur in a horizontal length of 12π?

Answer:

3

Explanation:

Step1: Recall the period - cycle relationship

The number of cycles $n$ is given by the formula $n=\frac{\text{total length}}{\text{period}}$.

Step2: Substitute the given values

We know that the total length is $12\pi$ and the period is $4\pi$. So $n = \frac{12\pi}{4\pi}$.

Step3: Simplify the expression

$\frac{12\pi}{4\pi}=3$.