jackson takes a marker and draws an arrow at the top of his yo - yo, pointing it toward the string when it…

jackson takes a marker and draws an arrow at the top of his yo - yo, pointing it toward the string when it is all wound up. the location of the arrow on the yo - yo can be represented by a cosine function. the function that represents the location of the arrow is f(x)=2cos(8πx)+2, where x represents time in seconds, and f(x) represents the vertical distance in inches that the arrow is from the lowest point on the yo - yo. how many times does the yo - yo rotate in 1 second? 8 times 8π times 4 times 16 times

jackson takes a marker and draws an arrow at the top of his yo - yo, pointing it toward the string when it is all wound up. the location of the arrow on the yo - yo can be represented by a cosine function. the function that represents the location of the arrow is f(x)=2cos(8πx)+2, where x represents time in seconds, and f(x) represents the vertical distance in inches that the arrow is from the lowest point on the yo - yo. how many times does the yo - yo rotate in 1 second? 8 times 8π times 4 times 16 times

Answer

Explanation:

Step1: Recall cosine - function period formula

For a cosine function of the form $y = A\cos(Bx - C)+D$, the period $T$ is given by $T=\frac{2\pi}{B}$. In the function $f(x)=2\cos(8\pi x)+2$, $B = 8\pi$.

Step2: Calculate the period

Substitute $B = 8\pi$ into the period formula $T=\frac{2\pi}{B}$. So, $T=\frac{2\pi}{8\pi}=\frac{1}{4}$ seconds.

Step3: Find the number of rotations per second

The number of rotations per second is the reciprocal of the period. If the period $T=\frac{1}{4}$ seconds, then the number of rotations per second $n=\frac{1}{T}$. So, $n = 4$ times.

Answer:

C. 4 times