Knowledge Check
Suppose that the height above ground of a person sitting on a Ferris wheel is described by the following.
\[
h(t)=17.6-15.5 \cos \left(\frac{2 \pi}{5} t\right)
\]

In this equation, $h(t)$ is the height above ground (in meters) and $t$ is the time (in minutes). The ride begins at $t=0$ minutes.

During the first 5 minutes of the ride, when will the person be 11 meters above the ground?
Do not round any intermediate computations, and round your answer(s) to the nearest hundredth of a minute. (If there is more than one answer, enter additional answers with the "or" button.)
\[
\mathrm{t}=\square \text { minutes }
\]
맘

Step 1 ：Set the height function equal to 11: \(11 = 17.6 - 15.5 \cos\left(\frac{2\pi}{5}t\right)\)

Step 2 ：Rearrange the equation to isolate the cosine function: \(15.5 \cos\left(\frac{2\pi}{5}t\right) = 17.6 - 11\)

Step 3 ：Simplify the right side of the equation: \(15.5 \cos\left(\frac{2\pi}{5}t\right) = 6.6\)

Step 4 ：Divide both sides by 15.5 to solve for the cosine function: \(\cos\left(\frac{2\pi}{5}t\right) = \frac{6.6}{15.5}\)

Step 5 ：Simplify the right side of the equation: \(\cos\left(\frac{2\pi}{5}t\right) = 0.425806\)

Step 6 ：Use the inverse cosine function to solve for \(\frac{2\pi}{5}t\): \(\frac{2\pi}{5}t = \arccos(0.425806)\)

Step 7 ：Solve for t: \(t = \frac{5}{2\pi} \arccos(0.425806)\)

Step 8 ：Calculate the value of t: \(t = \frac{5}{2\pi} * 1.094\)

Step 9 ：Simplify to find the first time when the person is 11 meters above the ground: \(t = 0.87\) minutes

Step 10 ：Find the second time within the first 5 minutes when the person is 11 meters above the ground: \(t = 5 - 0.87\)

Step 11 ：Simplify to find the second time when the person is 11 meters above the ground: \(t = 4.13\) minutes

Step 12 ：The person will be 11 meters above the ground at approximately \(\boxed{0.87}\) minutes and \(\boxed{4.13}\) minutes