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Math Help - Finding the period of a trigonmetic sine curve

  1. #1
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    Finding the period of a trigonmetic sine curve

    Hi Guys!

    I am new to this forum, this being my first ever post.

    The problem:

    I have a problem with calculating the period of a sine curve.
    I know the answer to the question - I know how to solve it (or so I thought) but the answer I arrive at doesn't match the one I know (think?!) is right.

    I was hoping somebody could guide me through to get the answer I'm looking for?

    The question:

    Involves finding the period for the function:

    h = 35 + 25sin(36t-90)

    The h is relative to the height.
    The t is relative to time in minutes.

    The function is a model of a fairground big-wheel turning.
    I have plotted this on a graph and have found the time it takes for the big wheel to do one revolution is 10 minutes.

    I thought the formula to calculate the period from the above was:

    T=((2*pi)/36) = 0.174533

    But how can that be the period when I know from my graphs etc that it takes 10 minutes to do one revolution?

    I then thought the 0.174533 might be the frequency, but the reciprocal of the frequency should be period (I'm right on that - right?), but the reciprocal of 0.174533 is 5.73.

    I have been on this for over 2 days now, almost non-stop and can't fathom it out. The closest I can get is by multiplying my answer 0.174533 by 60 to get 10.47.

    This has really got me wound up - please help!
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  2. #2
    MHF Contributor Amer's Avatar
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    Jordan
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    Quote Originally Posted by MaverickUK82 View Post
    Hi Guys!

    I am new to this forum, this being my first ever post.

    The problem:

    I have a problem with calculating the period of a sine curve.
    I know the answer to the question - I know how to solve it (or so I thought) but the answer I arrive at doesn't match the one I know (think?!) is right.

    I was hoping somebody could guide me through to get the answer I'm looking for?

    The question:

    Involves finding the period for the function:

    h = 35 + 25sin(36t-90)

    The h is relative to the height.
    The t is relative to time in minutes.

    The function is a model of a fairground big-wheel turning.
    I have plotted this on a graph and have found the time it takes for the big wheel to do one revolution is 10 minutes.

    I thought the formula to calculate the period from the above was:

    T=((2*pi)/36) = 0.174533

    But how can that be the period when I know from my graphs etc that it takes 10 minutes to do one revolution?

    I then thought the 0.174533 might be the frequency, but the reciprocal of the frequency should be period (I'm right on that - right?), but the reciprocal of 0.174533 is 5.73.

    I have been on this for over 2 days now, almost non-stop and can't fathom it out. The closest I can get is by multiplying my answer 0.174533 by 60 to get 10.47.

    This has really got me wound up - please help!
    it is the same how you find t=10 min anyway


    \frac{2\pi}{36 } pi here not 22/7 pi equal 180 degree that's you fault so

    \frac{2\pi}{36 } =\frac{360}{36} = 10
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  3. #3
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    Brilliant... so it was working in radians and just needed to be in degrees! Excellent!

    I don't however, understand your comment:
    "pi here not 22/7 pi equal 180 degree that's you fault so".

    where did the 22/7 pi come from?
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  4. #4
    MHF Contributor Amer's Avatar
    Joined
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    Jordan
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    Quote Originally Posted by MaverickUK82 View Post
    Brilliant... so it was working in radians and just needed to be in degrees! Excellent!

    I don't however, understand your comment:
    "pi here not 22/7 pi equal 180 degree that's you fault so".

    where did the 22/7 pi come from?
    I mean when you find the period in this

    Quote Originally Posted by MaverickUK82 View Post
    I thought the formula to calculate the period from the above was:

    T=((2*pi)/36) = 0.174533
    you sub pi value 22/7 but you should sub 180 instead of 22/7
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  5. #5
    Senior Member pacman's Avatar
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    pi is approximately equal to 22/7, BUT we are converting from RADIANS measure to DEGREES measure, MHF Amer is right in his comment . . . that is 2 pi rad = 360 degrees.
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  6. #6
    Member
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    Thanks guys - get it now - reps to both of you!
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