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.
Answers
Steve
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
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