Hi,
This is a ferris wheel question, which I believe is quite common in trig lessons. The wheel is 135 meters high, and turns at a constant speed of 30 minutes for one complete cycle.
The height as a function of time can be written as h(t) = a + b cos(ct). I need to find the coefficients for a, b and c. C is in radians and the wheel starts moving at t=0.
I can get as far as solving for c, which works out to be pi/15. But I am struggling with a and b.
I have been told that h(0) = 0: a + b = 0. And that h(15) = a - b = 135. But I don't understand why these statements are true. For example why do we add a + b in the first statement when h(0) = 0, and why do we subtract b from a in the second statement?
I'm also told that a = - b = 135/2. But I 'm not sure why we have to divide 135 by 2.
Any explanation would be appreciated. As you can see I've been given the answer, but I don't fully understand the steps to arrive at the answer.
Thank you.
This is a ferris wheel question, which I believe is quite common in trig lessons. The wheel is 135 meters high, and turns at a constant speed of 30 minutes for one complete cycle.
The height as a function of time can be written as h(t) = a + b cos(ct). I need to find the coefficients for a, b and c. C is in radians and the wheel starts moving at t=0.
I can get as far as solving for c, which works out to be pi/15. But I am struggling with a and b.
I have been told that h(0) = 0: a + b = 0. And that h(15) = a - b = 135. But I don't understand why these statements are true. For example why do we add a + b in the first statement when h(0) = 0, and why do we subtract b from a in the second statement?
I'm also told that a = - b = 135/2. But I 'm not sure why we have to divide 135 by 2.
Any explanation would be appreciated. As you can see I've been given the answer, but I don't fully understand the steps to arrive at the answer.
Thank you.