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Math Help - Find the equation of the curve given that...

  1. #1
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    Find the equation of the curve given that...

    Can anyone solve the question in this attachement, try to show working where possible so i can see what you have done.

    question attached
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  2. #2
    Senior Member apcalculus's Avatar
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    Quote Originally Posted by duckegg View Post
    Can anyone solve the question in this attachement, try to show working where possible so i can see what you have done.

    question attached
    The question is:

    \frac{dy}{dt} = 3sint

    when t=25 degrees , y = 2. Find the equation of the curve.

    Separate variables:

    1 dy = 3 sint dt

    Integrate both sides:
    y = -3 cost + C

    Plug in t=25 y=2 (Just remember that t is in degrees when you evaluate in your graphing calculator, and not in radians)
    2 = -3cos 25 + C

    Solve for C:
    C = 2 + 3cos25

    So the curve has equation y = -3cost(t) + 3 cos(25) + 2

    To check, differentiate and evaluate.

    Good luck!
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