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Can someone help me with some sine and cosine stuff, please?

Question

anonymous · Answer

Question 1:
The blades of a windmill turn on an axis that is 35 feet above the ground. The blades are 10 feet long and complete two rotations every minute. Which of the following equations can be used to model h, the height in feet of the end of one blade, as a function of time, t, in seconds? Assume that the blade is pointing to the right, parallel to the ground at t = 0 seconds, and that the windmill turns counterclockwise at a constant rate.

anonymous · Answer

Which is the right answer?
$$h=-10\sin(\frac{ \pi }{ 15 } t)+35$$
$$h=-10\sin(\pi  t)+35$$
$$h=10\sin(\frac{ \pi }{ 15 } t)+35$$
$$h=10\sin(\pi t)+35$$

anonymous · Answer

D

anonymous · Answer

Can you tell me how you got that answer?

anonymous · Answer

I ask because the assignment told me it was incorrect.

anonymous · Answer

it said D was wrong? Sure, so 35 is the mid line or the height above ground. that's the same for all the possible answers. The blades are 10 ft long. So the amplitude is 10 and it says they start at the 0degree mark and go counterclockwise. This means on the graph, it starts on the midline and goes up first. It's pi because it says it makes 2 rotations every minute. So your period is 2=2pi/B. If you solve for B, you get pi.

anonymous · Answer

That's almost exactly how I solved it and was the reason I chose D. I personally don't understand why it's wrong either.

anonymous · Answer

It could be C. If the blade spends twice in a minute, it would be 30 seconds. 30=2pi/B=pi/15. That's the only thing I can think of. Did it tell you the right answer?

anonymous · Answer

Sorry for the delay, no unfortunately it didn't, though what you said makes sense.