Results 1 to 5 of 5

Math Help - Radian Measure?

  1. #1
    Member
    Joined
    Oct 2008
    Posts
    157

    Radian Measure?

    This question is something to do with radian measure. I've never studied this before (I understand a few of the formulas generally used with no idea how they are applied) and want to solve this question:

    Two points P and Q lie on a circle with centre O. The radius of the circle is r cm and angle POQ = \theta radians. The length of the arc PQ is 6 cm and the area of the sector PQ is 22.5cm^2.
    Find the values of r and \theta. [5]

    Any help towards answering this is greatly appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,629
    Thanks
    430
    Quote Originally Posted by db5vry View Post
    This question is something to do with radian measure. I've never studied this before (I understand a few of the formulas generally used with no idea how they are applied) and want to solve this question:

    Two points P and Q lie on a circle with centre O. The radius of the circle is r cm and angle POQ = \theta radians. The length of the arc PQ is 6 cm and the area of the sector PQ is 22.5cm^2.
    Find the values of r and \theta. [5]

    Any help towards answering this is greatly appreciated.
    arc length, s = r\theta , \theta is in radians

    sector area, A = \frac{r^2 \theta}{2} , \theta in radians



    A = \frac{r^2 \theta}{2} = \frac{r \cdot r\theta}{2} = \frac{r \cdot s}{2}

    r = \frac{2A}{s}

    evaluate r, then go back to either of the original equations and solve for \theta.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,520
    Thanks
    1404
    Quote Originally Posted by db5vry View Post
    This question is something to do with radian measure. I've never studied this before (I understand a few of the formulas generally used with no idea how they are applied) and want to solve this question:

    Two points P and Q lie on a circle with centre O. The radius of the circle is r cm and angle POQ = \theta radians. The length of the arc PQ is 6 cm and the area of the sector PQ is 22.5cm^2.
    Find the values of r and \theta. [5]

    Any help towards answering this is greatly appreciated.
    A radian is a length of the radius on the circumference.

    You're told the radius is r and that the length of the arc PQ is 6\textrm{bf}.

    Therefore the angle \theta, in radians, is \frac{6}{r}.

    The area of a sector, if the angle is given in radians, is

    \frac{\theta}{2\pi}\pi r^2 = \frac{\theta}{2}r^2.

    We know that \theta = \frac{6}{r} and that the area is 22.5\textrm{cm}^2.

    So \frac{\frac{6}{r}}{2}r^2 = 22.5

    \frac{3}{r}r^2 = 22.5

    3r = 22.5

    r = 67.5\textrm{cm}.


    From this, we can see \theta = \frac{6}{67.5}^C.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,629
    Thanks
    430
    Quote Originally Posted by Prove It View Post
    A radian is a length of the radius on the circumference.

    You're told the radius is r and that the length of the arc PQ is 6\textrm{bf}.

    Therefore the angle \theta, in radians, is \frac{6}{r}.

    The area of a sector, if the angle is given in radians, is

    \frac{\theta}{2\pi}\pi r^2 = \frac{\theta}{2}r^2.

    We know that \theta = \frac{6}{r} and that the area is 22.5\textrm{cm}^2.

    So \frac{\frac{6}{r}}{2}r^2 = 22.5

    \frac{3}{r}r^2 = 22.5

    3r = 22.5

    r = 67.5\textrm{cm}. correction, r = 7.5 cm


    From this, we can see \theta = \frac{6}{67.5}^C.
    .
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,520
    Thanks
    1404
    Quote Originally Posted by skeeter View Post
    .
    Oops... Duh...

    I was just testing you :P
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Radian Measure
    Posted in the Trigonometry Forum
    Replies: 7
    Last Post: July 17th 2011, 05:30 PM
  2. Radian measure
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: November 24th 2009, 03:59 PM
  3. Radian Measure
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: November 24th 2009, 03:10 AM
  4. Radian Measure?
    Posted in the Algebra Forum
    Replies: 1
    Last Post: May 9th 2009, 09:34 AM
  5. Radian Measure 2
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: December 22nd 2008, 11:38 PM

Search Tags


/mathhelpforum @mathhelpforum