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 hh above the ground of a seat under which she put a location sensor (in dark brown, picture below):

h(t)=12[sin(π4tπ4)]+45 h(t)=\displaystyle\dfrac{1}{2}\cdot\left[\sin\left(\dfrac{\pi}{4}t-\dfrac{\pi}{4}\right)\right]+\dfrac{4}{5}

where hh is expressed in metres and time tt in seconds.

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

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