Question

The height in inches about the ground of the tip of the hour hand is a function, h(t), of the time (t), in hours. The hour hand is 6 inches long and the middle of the clock face is 68 inches about the ground. Identify the period, midline, and amplitude of the function.

Answer 1

since the center of the clock is 68" above the ground, you know the function will be

h(t) = 6*cos(kt) + 68

why? because at t=0, it's 12:00, and the hour hand is at its max height, 6" above center.

Now, we know that at t=12, it is back on top, so the period is 12:

h(t) = 6cos(2pi/12 t) + 68