# Merry-go-round: cyclic equation to model the distance

Brenna's mom, Mrs. Herstone, is watching Brenna playing at the park. Some children are pushing Brenna around the merry-go-round. Mrs. Herstone decides to take some data, so she started her stopwatch. At 3.5 seconds Brenna is farthest from Mrs. Herstone 26 feet away. When the stopwatch reads 4.2 seconds, Brenna is closest at 12 feet away. Find a cyclic equation that models the distance Brenna is from Mrs. Herstone over time if the merry-go-round is spinning at a constant rate.

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#### Solution Preview

The general form for the cyclic equation that models the distance, y, Brenna is from Mrs. Herstone over time, t, is y = A sin [ B (t - h) ] + k.

Where A is the amplitude,

B is 2pi / period

h is the horizontal shift

k is the vertical shift

We will find A, B, h ...

#### Solution Summary

A step-by-step solution with equations and computations is provided in the Word file.