a spinning top can be represented by a sine function. the top completes 12 whole rotations in a time period…

a spinning top can be represented by a sine function. the top completes 12 whole rotations in a time period of 2π seconds. which function rule could model this situation? o f(x)=sin(1/12x) o f(x)=12sin(x) o f(x)=sin(12x) o f(x)=sin(x)+12

a spinning top can be represented by a sine function. the top completes 12 whole rotations in a time period of 2π seconds. which function rule could model this situation? o f(x)=sin(1/12x) o f(x)=12sin(x) o f(x)=sin(12x) o f(x)=sin(x)+12

Answer

Explanation:

Step1: Recall the general form of a sine - function

The general form of a sine - function is $y = A\sin(Bx - C)+D$, where the period $T=\frac{2\pi}{B}$.

Step2: Determine the period of the spinning top

The top completes 12 rotations in $2\pi$ seconds. The period of one rotation is the time for one full cycle. If 12 rotations occur in $2\pi$ seconds, then the period $T$ of one rotation is $\frac{2\pi}{12}=\frac{\pi}{6}$ seconds.

Step3: Find the value of B

We know that $T = \frac{2\pi}{B}$. Substituting $T=\frac{\pi}{6}$ into the formula, we get $\frac{\pi}{6}=\frac{2\pi}{B}$. Cross - multiplying gives $\pi B = 12\pi$, so $B = 12$.

Step4: Identify the function

Since $A = 1$, $C = 0$, and $D = 0$ (no vertical stretch, phase shift, or vertical shift mentioned), the function is $f(x)=\sin(12x)$.

Answer:

$f(x)=\sin(12x)$