Results 1 to 2 of 2
Like Tree2Thanks
  • 2 Post By zemozamster

Thread: Circle sector

  1. #1
    Junior Member
    Joined
    Aug 2016
    From
    U.K.
    Posts
    34

    Circle sector

    Hi , I just started with radian measure an have this



    And now i can't figure out how to do point b) ("Using AOC show that R sin theta = ..." part) , I mean I'm not sure if I understand how I should go about this type of question, why is there sin theta ? using triangle area formula gets me nowhere , any advice how i should approach this particular question?
    Attached Thumbnails Attached Thumbnails Circle sector-img_1722.jpg   Circle sector-img_1723.jpg  
    Last edited by AbYz; Aug 6th 2017 at 06:22 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Aug 2017
    From
    Finland
    Posts
    27
    Thanks
    9

    Re: Circle sector

    Since OT = R and CT = r (because of radii of corresponding circles), OC = OT-CT = R-r
    Notice that OCE is right-angled triangle with OC = R-r, CE = r, COE = theta, and OEC = pi/2.
    Therefore, sin(COE) = sin(theta) = CE/OC = r/(R-r). Simplifying this yields the required expression.

    For the clarity of reading,
    OC= OT - CT = R-r
    Since OCE is right-angle triangle with OEC \angle = \pi/2,
    \sin(\theta) = CE/OC = r/(R-r)
    \frac{\sin(\theta)}{1} = \frac{r}{R-r} \implies \frac{\sin(\theta)}{1-\sin(\theta)} = \frac{r}{R} \implies R\sin(\theta) = r(1+\sin(\theta))
    Thanks from HallsofIvy and AbYz
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Sector of circle radius and areas
    Posted in the Geometry Forum
    Replies: 5
    Last Post: Feb 18th 2013, 11:05 PM
  2. Inscribe a circle into a sector?
    Posted in the Geometry Forum
    Replies: 2
    Last Post: Feb 16th 2013, 11:13 AM
  3. Right circular cone to a sector of a circle.
    Posted in the Geometry Forum
    Replies: 2
    Last Post: Aug 11th 2012, 01:51 AM
  4. area of a sector of a circle
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: Jun 28th 2010, 06:41 AM
  5. Inscribe a circle into a sector
    Posted in the Geometry Forum
    Replies: 3
    Last Post: Mar 7th 2010, 02:41 PM

/mathhelpforum @mathhelpforum