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Math Help - Radian Question.

  1. #1
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    Radian Question.

    Just got done reading the chapter... Want to make sure I have this right....

    IF Circumference = 2(pi)r
    Let cir = 360 deg.
    So that 360 deg = 2(pi)r

    And 180 deg = (pi)r

    IF r = 10
    then 180 = (pi)10

    Hence half of a cirlce with radius of 10 has an arc measure of 10(pi).....

    Is this correct?


    And if I wanted to find An arc measure of angle 70 deg I would
    solve for x
    180x = 70
    x = 70/180 = 7/18
    then
    70 = (7/18)(Pi)(10)
    If radius is 10....
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    Quote Originally Posted by Mike012 View Post
    So that 360 deg = 2(pi)r
    One is the measure of degrees inside a circle the other is the length around the circle.

    You can say 360^{\circ} = 2\pi^c

    Or C= 2\pi r when r=10 \implies C =2\times \pi \times 10 \approx 62.8
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    you repeated what I said....
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    Quote Originally Posted by Mike012 View Post
    you repeated what I said....
    you said 360 = 2\pi r ; that is not true.

    360 degrees = 2\pi radians ... the radius doesn't matter.


    an angle \theta measured in radians is defined as \displaystyle \theta = \frac{s}{r} , where s is the arclength of the intercepted arc.

    so, for a whole circle, \displaystyle \theta = \frac{2\pi r}{r} = 2\pi
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    Quote Originally Posted by Mike012 View Post
    And if I wanted to find An arc measure of angle 70 deg I would
    solve for x
    180x = 70
    x = 70/180 = 7/18
    then
    70 = (7/18)(Pi)(10)
    If radius is 10....
    I measure an arc length as L = \frac{\theta}{360}\times 2\pi r

    In your case, r=10, \theta = 70  , L = \frac{70}{360}\times 2\pi \times 10=\dots
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  6. #6
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    Quote Originally Posted by Mike012 View Post
    Just got done reading the chapter... Want to make sure I have this right....

    IF Circumference = 2(pi)r
    Let cir = 360 deg.
    So that 360 deg = 2(pi)r

    And 180 deg = (pi)r
    No r comes after the circumference equation since the 1 radian is the angle subtended by an arc of length equal to the radius. If we want to find out how many radians are in a full circle we can divide the circumference by the number of radii - \theta = \dfrac{C}{r} = \dfrac{2\pi r}{r} = 2\pi

    Then set this equal to 360 degrees to give \pi rad = 180^{\circ}

    IF r = 10
    then 180 = (pi)10
    No, angle measurement is independent of the radius. 180^o = \pi


    Hence half of a cirlce with radius of 10 has an arc measure of 10(pi).....

    Is this correct?
    Yes. Arc length = Angle * radius or l = \theta r


    And if I wanted to find An arc measure of angle 70 deg I would
    solve for x
    180x = 70
    x = 70/180 = 7/18
    then
    70 = (7/18)(Pi)(10)
    If radius is 10....
    You'd find 70 degrees in radians

    1 degree = \dfrac{\pi}{\180} rad so 70 degrees is \dfrac{7\pi}{18} (note I have multiplied by pi when finding the angle)

    The sub in

    l = 10 \cdot \dfrac{7\pi}{18}
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