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anonymous

  • one year ago

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?

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  1. amistre64
    • one year ago
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    what is the value when t=0?

  2. amistre64
    • one year ago
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    cos has a normal period of 2pi so when does pi/14 * t = 2pi?

  3. anonymous
    • one year ago
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    I know that a full revolution around the unit circle is equal to 2pi

  4. amistre64
    • one year ago
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    then cos(2pi) is one complete revolution therefore, we simply need to determine when pi/14*t = 2pi

  5. anonymous
    • one year ago
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    How would I find that, though?

  6. amistre64
    • one year ago
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    simple algebra ....

  7. amistre64
    • one year ago
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    multiply both sides by .... what?

  8. anonymous
    • one year ago
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    pi/14?

  9. amistre64
    • one year ago
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    well, 14/pi would wipe out the pi/14 so ... lets say t = 2pi * 14/pi makes one full revolution

  10. anonymous
    • one year ago
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    Okay, I understand. What do I do from there?

  11. amistre64
    • one year ago
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    simplify .. what is 2pi * 14/pi?

  12. anonymous
    • one year ago
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    Would pi cancel out?

  13. amistre64
    • one year ago
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    yes, even tho thats a bad word to apply ... pi/pi = 1, so there is nothing to actually 'cancel'. but yeah

  14. anonymous
    • one year ago
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    Alright, so when pi/pi = 1, that leaves 2 *14 = 28

  15. amistre64
    • one year ago
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    correct, so it takes a time period of 28 to make one full revolution right?

  16. anonymous
    • one year ago
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    Right.

  17. amistre64
    • one year ago
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    so part 2 is done, what was part 1?

  18. anonymous
    • one year ago
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    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

  19. amistre64
    • one year ago
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    25+31 = 56 .. i agree now what do you know about the min and max of a cos(u) ?

  20. anonymous
    • one year ago
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    I don't know anything about that

  21. amistre64
    • one year ago
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    really? you have unit circle right?

  22. amistre64
    • one year ago
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    or at least are able to graph y = cos(x)

  23. anonymous
    • one year ago
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    Yes, but I'm not technically in trig. I'm actually in Algebra 2. This is just an intro to trig, I guess

  24. anonymous
    • one year ago
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    I'm not great at graphing either

  25. amistre64
    • one year ago
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    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

  26. amistre64
    • one year ago
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    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?

  27. anonymous
    • one year ago
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    I'm so sorry, but I have absolutely no clue

  28. amistre64
    • one year ago
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    hmm, cos(pi/14*t) has a minimum value of -1. so use it 25(min of cos) + 31 gives us?

  29. anonymous
    • one year ago
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    6?

  30. amistre64
    • one year ago
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    25(-1) + 31 is 6 yes

  31. anonymous
    • one year ago
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    Thanks for your help!

  32. amistre64
    • one year ago
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    good luck

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