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egbeach

  • one year ago

Eliminate the parameter. x = 4 cos t, y = 4 sin t

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  1. jtvatsim
    • one year ago
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    For most of these questions the strategy is to solve one equation for t and plug this into the remaining equation, however, that will be very messy for this one. Instead, you will need to be a little clever and use the fact that \[\cos^2 t +\sin^2 t = 1. \] Here's how...

  2. jtvatsim
    • one year ago
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    Notice that \[x = 4\cos t \Rightarrow x^2 = 16\cos^2 t\]

  3. jtvatsim
    • one year ago
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    Also, \[y = 4\sin t \Rightarrow y^2 = 16\sin^2 t \]

  4. jtvatsim
    • one year ago
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    Then, (again being very clever) notice that we can add these new equations together to get \[x^2 + y^2 = 16\cos^2 t + 16 \sin^2 t \] but this is just \[x^2 + y^2 = 16(\cos^2 t + \sin^2 t) = 16(1) = 16 \] There the parameter is gone!

  5. jtvatsim
    • one year ago
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    \[x^2 + y^2 = 16\]

  6. jtvatsim
    • one year ago
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    Any questions? That was a pretty tricky method. @egbeach

  7. egbeach
    • one year ago
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    Thank you!

  8. jtvatsim
    • one year ago
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    No problem. Good luck!

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