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Math Help - Trig Word Problem

  1. #1
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    Trig Word Problem

    Hey, just stopping by, need some help on a review question and any help would be appreciated.

    Question:

    The following describes the height in, in meters, of a cart on a ferris wheel as a function of time, in seconds.

    H = 10sin[30(t-3)]+11.5

    Determine the time it takes a person to reach a height of 16m.


    I know to plug 16 in for H, but what do I do from there to solve for t?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by RyanOwnage View Post
    Hey, just stopping by, need some help on a review question and any help would be appreciated.

    Question:

    The following describes the height in, in meters, of a cart on a ferris wheel as a function of time, in seconds.

    H = 10sin[30(t-3)]+11.5

    Determine the time it takes a person to reach a height of 16m.


    I know to plug 16 in for H, but what do I do from there to solve for t?
    well, you begin by solving for the sine. then take the arcsine to solve for what was being sined. you'd end up with:

    30(t - 3) = arcsin(...)

    you can find the arcsine from your calculator and then it would be easy to solve for t from there

    can you continue?
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  3. #3
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    Bit confused

    Could you possibly show me the first couple of steps?

    Thanks again.
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by RyanOwnage View Post
    Bit confused

    Could you possibly show me the first couple of steps?

    Thanks again.
    16 = 10 \sin [30(t - 3)] + 11.5 ......subtract 11.5 from both sides

    \Rightarrow 4.5 = 10 \sin [30(t - 3)] ...........divide both sides by 10

    \Rightarrow 0.45 = \sin [30(t - 3)] ..........take the arcsine of both sides

    \Rightarrow 30(t - 3) = \arcsin (0.45)
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  5. #5
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    Thank you very much, got it solved
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