anonymous
  • 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?
Trigonometry
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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amistre64
  • amistre64
what is the value when t=0?
amistre64
  • amistre64
cos has a normal period of 2pi so when does pi/14 * t = 2pi?
anonymous
  • anonymous
I know that a full revolution around the unit circle is equal to 2pi

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amistre64
  • amistre64
then cos(2pi) is one complete revolution therefore, we simply need to determine when pi/14*t = 2pi
anonymous
  • anonymous
How would I find that, though?
amistre64
  • amistre64
simple algebra ....
amistre64
  • amistre64
multiply both sides by .... what?
anonymous
  • anonymous
pi/14?
amistre64
  • amistre64
well, 14/pi would wipe out the pi/14 so ... lets say t = 2pi * 14/pi makes one full revolution
anonymous
  • anonymous
Okay, I understand. What do I do from there?
amistre64
  • amistre64
simplify .. what is 2pi * 14/pi?
anonymous
  • anonymous
Would pi cancel out?
amistre64
  • amistre64
yes, even tho thats a bad word to apply ... pi/pi = 1, so there is nothing to actually 'cancel'. but yeah
anonymous
  • anonymous
Alright, so when pi/pi = 1, that leaves 2 *14 = 28
amistre64
  • amistre64
correct, so it takes a time period of 28 to make one full revolution right?
anonymous
  • anonymous
Right.
amistre64
  • amistre64
so part 2 is done, what was part 1?
anonymous
  • 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
  • amistre64
25+31 = 56 .. i agree now what do you know about the min and max of a cos(u) ?
anonymous
  • anonymous
I don't know anything about that
amistre64
  • amistre64
really? you have unit circle right?
amistre64
  • amistre64
or at least are able to graph y = cos(x)
anonymous
  • 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
  • anonymous
I'm not great at graphing either
amistre64
  • 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
  • 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
  • anonymous
I'm so sorry, but I have absolutely no clue
amistre64
  • amistre64
hmm, cos(pi/14*t) has a minimum value of -1. so use it 25(min of cos) + 31 gives us?
anonymous
  • anonymous
6?
amistre64
  • amistre64
25(-1) + 31 is 6 yes
anonymous
  • anonymous
Thanks for your help!
amistre64
  • amistre64
good luck

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