- anonymous

Please help. I have no idea what to do with this trig problem.
~~~
Sandra is riding the Ferris wheel, and her height can be modeled by the equation H(t) = 25 cos(pi/14 * t) + 31, where H represents the height of the person above the ground in feet at t seconds.
Part 1: How far above the ground is Sandra before the ride begins?
Part 2: How long does the Ferris wheel take to make one complete revolution?
Part 3: Assuming Sandra begins the ride at the top, how far from the ground is the edge of the Ferris wheel when Sandra's height above the ground reaches a minimum?

- katieb

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- amistre64

what is the value when t=0?

- amistre64

cos has a normal period of 2pi
so when does pi/14 * t = 2pi?

- anonymous

I know that a full revolution around the unit circle is equal to 2pi

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## More answers

- amistre64

then cos(2pi) is one complete revolution
therefore, we simply need to determine when pi/14*t = 2pi

- anonymous

How would I find that, though?

- amistre64

simple algebra ....

- amistre64

multiply both sides by .... what?

- anonymous

pi/14?

- amistre64

well, 14/pi would wipe out the pi/14 so ... lets say t = 2pi * 14/pi makes one full revolution

- anonymous

Okay, I understand. What do I do from there?

- amistre64

simplify .. what is 2pi * 14/pi?

- anonymous

Would pi cancel out?

- amistre64

yes, even tho thats a bad word to apply ...
pi/pi = 1, so there is nothing to actually 'cancel'. but yeah

- anonymous

Alright, so when pi/pi = 1, that leaves 2 *14 = 28

- amistre64

correct, so it takes a time period of 28 to make one full revolution right?

- anonymous

Right.

- amistre64

so part 2 is done, what was part 1?

- anonymous

Using the equation, I substituted 0 in for the value of t, since the ride has not started yet. The new equation will then look like, H(0) = 25 cos(pi/14 * t) + 31. Simplifying, the height of Sandra when t = 0 is 56 feet

- amistre64

25+31 = 56 .. i agree
now what do you know about the min and max of a cos(u) ?

- anonymous

I don't know anything about that

- amistre64

really? you have unit circle right?

- amistre64

or at least are able to graph y = cos(x)

- anonymous

Yes, but I'm not technically in trig. I'm actually in Algebra 2. This is just an intro to trig, I guess

- anonymous

I'm not great at graphing either

- amistre64

well, the unit circle, tells us cosine from left to right ...
|dw:1442188466506:dw|
unit is another way of saying 1, the unit circle has a radius of 1

- amistre64

cos alternates from 1 to -1 to 1 to -1 ... etc
so its max is 1, its min is -1
how can we use this in part3?

- anonymous

I'm so sorry, but I have absolutely no clue

- amistre64

hmm, cos(pi/14*t) has a minimum value of -1. so use it
25(min of cos) + 31 gives us?

- anonymous

6?

- amistre64

25(-1) + 31 is 6 yes

- anonymous

Thanks for your help!

- amistre64

good luck

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