Question

the function ( d(t)=2sin(t)+3 ) describes the vertical position, ( d ), in feet, of a swinging piñata over time, ( t ), in seconds ( (0leq tleq2pi) ). if lupes plan is to count 3 seconds and then take a swing at the piñata, approximately how many feet high will lupe need to aim?
a. 2.0
b. 3.0
c. 3.3
d. 4.0

Explanation:

Step1: Substitute \(t = 3\) into the function

Given \(d(t)=2\sin(t)+3\), when \(t = 3\), we have \(d(3)=2\sin(3)+3\).

Step2: Calculate the value of \(\sin(3)\)

We know that \(\sin(3)\approx0.1411\) (using a calculator in radian mode).

Step3: Calculate \(d(3)\)

Substitute \(\sin(3)\approx0.1411\) into \(d(3)=2\sin(3)+3\). Then \(d(3)\approx2\times0.1411 + 3\).

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Answer:

C. 3.3