Question

Please help. I have no idea what to do with this trig problem.

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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?

Answer 1

what is the value when t=0?

Answer 2

cos has a normal period of 2pi

so when does pi/14 * t = 2pi?

Answer 3

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

Answer 4

then cos(2pi) is one complete revolution

therefore, we simply need to determine when pi/14*t = 2pi

Answer 5

How would I find that, though?

Answer 6

simple algebra ....

Answer 7

multiply both sides by .... what?

Answer 8

pi/14?

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

Would pi cancel out?

Answer 13

yes, even tho thats a bad word to apply ...

pi/pi = 1, so there is nothing to actually 'cancel'. but yeah

Answer 14

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

Answer 15

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

Answer 16

Right.

Answer 17

so part 2 is done, what was part 1?

Answer 18

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

Answer 19

25+31 = 56 .. i agree

now what do you know about the min and max of a cos(u) ?

Answer 20

I don't know anything about that

Answer 21

really? you have unit circle right?

Answer 22

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

Answer 23

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

Answer 24

I'm not great at graphing either

Answer 25

well, the unit circle, tells us cosine from left to right ...



unit is another way of saying 1, the unit circle has a radius of 1

Answer 26

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?

Answer 27

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

Answer 28

hmm, cos(pi/14*t) has a minimum value of -1. so use it

25(min of cos) + 31 gives us?

Answer 29

6?

Answer 30

25(-1) + 31 is 6 yes

Answer 31

Thanks for your help!

Answer 32

good luck