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Math Help - trig word problem; sinusoidal function

  1. #1
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    trig word problem; sinusoidal function

    A piston in an engine moves up and down in a cylinder. The height, h centimetres, of the piston a t seconds is given by the formula h= 120 sin Pi t+ 200.
    -State amplitude & period
    -State max & min. heights of piston
    -How many complete cycles does the piston make in 30 min.

    I have no idea where to start. Is this the same as y=a sin k(x+c)? Should I graph the equation as is and go from there?

    Thanks in advance for any suggestions!

    W.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by sux@math View Post
    A piston in an engine moves up and down in a cylinder. The height, h centimetres, of the piston a t seconds is given by the formula h= 120 sin Pi t+ 200.
    -State amplitude & period
    -State max & min. heights of piston
    -How many complete cycles does the piston make in 30 min.

    I have no idea where to start. Is this the same as y=a sin k(x+c)? Should I graph the equation as is and go from there?

    Thanks in advance for any suggestions!

    W.
    Well for starters is this equation:
    h = 120 ~ sin(\pi t) + 200
    or
    h = 120 ~ sin(\pi t + 200)

    Please use parenthesis!

    -Dan
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  3. #3
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    Thanks for the quick reply! Um . . . I'm sorry, but the equation in my book has no parentheses! (it's kind of a crap correspondence course I am taking for Grade 11 Math)....

    It reads exactly how I typed it in my first post.
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by sux@math View Post
    A piston in an engine moves up and down in a cylinder. The height, h centimetres, of the piston a t seconds is given by the formula h= 120 sin Pi t+ 200.
    -State amplitude & period
    -State max & min. heights of piston
    -How many complete cycles does the piston make in 30 min.
    All right then, we read it almost without any parenthesis. The \pi t is obviously meant to be in the argument of the sine function; I will take the 200 as outside.
    h = 120 ~sin(\pi t) + 200

    The amplitude should be obvious, its 120 cm.

    The period of a function is how much time it takes for one oscillation. One oscillation of the sine function is 2\pi. So find when \pi t is 2 \pi:
    \pi T = 2 \pi \implies T = 2~s

    I'll leave it to you to determine the max and min heights.

    As to how many complete cycles are in a time period of 30 minutes, how many periods are in 30 minutes? (Remember that the period is in seconds, not minutes!)

    -Dan
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  5. #5
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    Thank you, Dan!!!
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