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Math Help - Help with Unit Circle Problem

  1. #1
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    Help with Unit Circle Problem

    My question reads

    "Suppose t is the length of the arc on the unit circle whose initial point is (1,0), and terminal point is P (x,y). If t=3.5, sketch on the unit circle below the approximate location of P(x,y)"

    Okay, I understand this part of the question, I know the point is in quadrant 3, etc.

    Then the question asks "find the x-coordinate and y-coordinate of P accurate to two decimal places"

    I have the answers, but I am dumbfounded as to how they were acquired.

    (.-94, .-35) are the coordinates.

    Any help would be much appreciated.

    Thank you
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by NYKnicks View Post
    My question reads

    "Suppose t is the length of the arc on the unit circle whose initial point is (1,0), and terminal point is P (x,y). If t=3.5, sketch on the unit circle below the approximate location of P(x,y)"

    Okay, I understand this part of the question, I know the point is in quadrant 3, etc.

    Then the question asks "find the x-coordinate and y-coordinate of P accurate to two decimal places"

    I have the answers, but I am dumbfounded as to how they were acquired.

    (.-94, .-35) are the coordinates.

    Any help would be much appreciated.

    Thank you
    Hi NYKnicks,

    I suppose you found where the point lies by determining what part of the circumference 3.5 was.

    \frac{3.5}{2 \pi}

    Now, that's how much of 360 degrees the point has traveled from (1, 0).

    \frac{3.5}{2 \pi}\left(360\right) \approx 200.54^{\circ}, which we'll call angle \theta.

    The point P(x, y) = P(\cos \theta, \sin \theta)

    Now find cos 200.54 and sin 200.54 and you have your coordinates.
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  3. #3
    MHF Contributor
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    Talking

    You are given the arc length, and you know that the radius is r = 1. Plug this into the arc-length formula to find the subtended angle \theta.

    Once you have the angle, use the fact that the x-value is the cosine on the unit circle, and the y-value is the sine.
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  4. #4
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    Wow, thanks for the quick replies guys!

    Understand now
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  5. #5
    Senior Member pacman's Avatar
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    It t = 3.5, then moving anti-clockwise with radius = r = 1, that is more that half of the circle of radius 1, half arc = pi = 3.1415 . . .

    So the point is in the 3rd quardant . . . .
    P(x,y) = P(cos 200.54, sin 200.54)
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