A Trigonometric Model In The Park

Geometry Level 4

Michaelle decided to go to the playground. She saw two boys at the swing set, composed of a board and two seats.

Michaelle obtained the following mathematical model for height \(h\) above the ground of a seat under which she put a location sensor (in dark brown, picture below):

\[ h(t)=\displaystyle\dfrac{1}{2}\cdot\left[\sin\left(\dfrac{\pi}{4}t-\dfrac{\pi}{4}\right)\right]+\dfrac{4}{5} \]

where \(h\) is expressed in metres and time \(t\) in seconds.

If the period of this motion is \(A\), the initial distance from the ground to the seat is \(B\), and the center of oscillation is \(C\), what is \(A+B+C\) (rounded to the nearest hundredth)?


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