I have the question and my answer below

Question

Can someone please double check my work? I got 7/8 on my answer for this...

Question: The height of a rider on the Star of Lake Tai Ferris wheel in China can be determined using the following equation:

h(t)=-67.5cos((2pi)/30t)+69.5

Assume that one full rotation takes 30 minutes. For how many minutes is the cabin 100 meters or more above ground?

Keep in mind that the cabin begins and ends two meters off of the ground, not quite at ground level.

Answer:

You set the equation to 100 and solve. I did this by doing 100= -67.5sin(pi/15t)+69.5=-67.5cos(pi/15t)+69.5. First you subtract 69.5 from all sides and you get 30.5 = -67.5sin(pi/15t)=-67.5cos(pi/15t). Then you divide -67.5 from all sides and you get 30.5/-67.5= cos(pi/15t)=sin(pi/15t). Now you continue solving for t by doing pi/15t=arcsin(30.5/67.5)=arccos(30.5/67.5) and then t=15/pi*arcsin(30.5/67.5)=15/pi*arccos(30.5/67.5). Now using our knowledge that inverse in and cosine functions only return values in a set value, we have to calculate the second value. To do this we will do t2-t1=t. t=(15)/pi*arccos(30.5/67.5)-(-(15)/pi*arccos(30.5/67.5)which simplifies to 2*(15)/pi*arccos(30.5/67.5) and plugging this into the calculator gives us about t=10.73 minutes. You can check your work by looking at a graph of the equation and when I did it shows that this is correct.

Answer 1

Hi Annie,

I did it twice and got the same answer you did.

Not sure whats wrong

Jim

Answer 2

There is no need to write down the terms containing sin((pi/15)*t). The problem only requires solving the equation 100=-67.5*cos((pi/15)*t) + 69.5

I suspect the deduction of one point came from writing down -67.5sin(pi/15t)+69.5=-67.5cos(pi/15t)+69.5