# 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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