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Math Help - Quick Question

  1. #1
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    Quick Question

    On the unit circle, if A is the area of the sector formed by a central angle of theta radians,
    then A = theta


    I don't understand this, can someone help?
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  2. #2
    Moo
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    Hello,

    Quote Originally Posted by gabrie30 View Post
    For a circle of radius 2, a central angle of 45 subtends an arc whose length s is 90.


    Is this true or false? Why?

    My guess is that its false and that the arc is (2X(PI/3))
    This is indeed false, but I would say the answer is pi/2.

    45/360=1/8

    The perimeter is 2*pi*2=4*pi

    --> length of the arc is (4*pi)/8
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  3. #3
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    Quote Originally Posted by gabrie30 View Post
    On the unit circle, if A is the area of the sector formed by a central angle of theta radians,
    then A = theta


    I don't understand this, can someone help?
    If you want to ask a new question, post it in a new thread. Do not simply edit over the old one.

    -Dan
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by gabrie30 View Post
    On the unit circle, if A is the area of the sector formed by a central angle of theta radians,
    then A = theta


    I don't understand this, can someone help?
    Your formula is off by a factor of 2.

    The angle \theta is a section of the circle. So the area of the wedge is proportional to the angle \theta.

    Thus
    \frac{\theta}{2 \pi} = \frac{A}{\pi (1)^2}
    (Remember this is the unit circle so r = 1.)

    A = \frac{\theta}{2}

    -Dan
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