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anonymous

  • 5 years ago

a circle of radius 5 centered at the point 2,1 and traced out counterclockwise

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  1. anonymous
    • 5 years ago
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    ok, what do you need to know about it?

  2. anonymous
    • 5 years ago
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    find parameters

  3. anonymous
    • 5 years ago
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    x = 2 + 5cos(t) y = 1 + 5sin(t) where t is between 0 and 2π

  4. anonymous
    • 5 years ago
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    how did you come up with that can u please show me?

  5. anonymous
    • 5 years ago
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    Circles are defined by the equation (x-a)^2 + (y-b)^2 = r^2 where (a, b) is the center and r is the radius.

  6. anonymous
    • 5 years ago
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    i understand that you plugged in the points into the equation and you got (x-2)^2 + (y-1)^2 = 5^2 . i don't understand what happend next

  7. anonymous
    • 5 years ago
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    Right. So if you remember that sin^2(x) + cos^2(x) = r^2 (a trig identity)

  8. anonymous
    • 5 years ago
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    If we want to rewrite this in terms of parametric we want (x-2)^2 = sin^2(t) and (y-1)^2 = cos^2(t) Solving each of these yields what I posted before and the 5 is just to factor for the radius.

  9. anonymous
    • 5 years ago
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    can you please show me how u solved for one of them (cos)

  10. anonymous
    • 5 years ago
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    The 5 is because if you want sin^2(t) + cos^2(t) [a trig identity that equals 1] to equal 25 (5^2) then you have to multiply the original equation by 25 so 25sin^2(t) + 25cos^2(t) = 5^2 (y-1)^2 = 25cos^2(t) so if you take the square root of both sides you'd get (y-1) = 5cos(t) and then adding 1 to both sides yields y = 1 + 5cos(t).

  11. anonymous
    • 5 years ago
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    if it is counterclockwise should cos be equal to x

  12. anonymous
    • 5 years ago
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    I think setting 0≤t≤2π handles the counterclockwise part (if you think about your unit circle this should make sense). I do know that parametric equations are not unique in that there are multiple ways to express the same shape with different parametric curves.

  13. anonymous
    • 5 years ago
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    okay thank you for your help

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