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Math Help - heights of objects

  1. #1
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    heights of objects

    The heights h (in feet) of two people in different seats on a ferris wheel can be modeled by h1=28cos10t+38 and h2=28cos(10(t-Pie/6))+38, 0 is less than or equal to t and 2 is greater than or equal to t. t is the time ( in minutes). When are the two people at the same height?

    this is another one that has been stumping me
    thanks again for the help
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  2. #2
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by belloway View Post
    The heights h (in feet) of two people in different seats on a ferris wheel can be modeled by h1=28cos10t+38 and h2=28cos(10(t-Pie/6))+38, 0 is less than or equal to t and 2 is greater than or equal to t. t is the time ( in minutes). When are the two people at the same height?

    this is another one that has been stumping me
    thanks again for the help

    h_1= 28\cos 10t + 38

    h_2= 28\cos 10\left(t-\frac{\pi}{6}\right) + 38

    same height

    h_1 = h_2

    28\cos 10 t +38 = 28\cos 10\left(t-\frac{\pi}{6}\right) + 38

    \cos 10t = \cos 10\left(t-\frac{\pi}{6}\right)

    use the identity

    \cos a-b = \cos a \cdot \cos b + \sin a \cdot \sin b

    after you use it and simplify you will get

    \cos 10 t = -\sqrt{3} \sin 10t

    \tan 10 t = \frac{-1}{\sqrt{3}}
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