Results 1 to 3 of 3

Math Help - Reciprocating Radians & more

  1. #1
    Senior Member DivideBy0's Avatar
    Joined
    Mar 2007
    From
    Melbourne, Australia
    Posts
    432

    Reciprocating Radians & more

    We have that

    1 Radian = \frac{180}{\pi} degrees

    Then isn't it true that

    \frac{1}{1}=1 Radians = \frac{\pi}{180} degrees?

    Also, I was reading in a precalc book that the area of a sector of a circle is \frac{1}{2} \times r^2 \times \theta, where \theta is the angle in radians. As I'm not used to using radians, I usually do \frac{r^2 \times \pi \times \Phi}{360} where \Phi is the angle in degrees. Can someone please explain slowly how to transfer from one to the other?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,903
    Thanks
    329
    Awards
    1
    Quote Originally Posted by DivideBy0 View Post
    We have that

    1 Radian = \frac{180}{\pi} degrees

    Then isn't it true that

    \frac{1}{1}=1 Radians = \frac{\pi}{180} degrees?
    So you are trying to say that
    1\text{ rad } = \frac{1}{1 \text{ rad }}??
    If you have an angle of \theta rad then it is equivalent to an angle of \theta \cdot \frac{180^o}{\pi~\text{rad}} degrees.

    If you have an angle of \theta degrees then it is equivalent to an angle of \theta \cdot \frac{\pi~\text{rad}}{180^o} rad.


    Quote Originally Posted by DivideBy0 View Post
    Also, I was reading in a precalc book that the area of a sector of a circle is \frac{1}{2} \times r^2 \times \theta, where \theta is the angle in radians. As I'm not used to using radians, I usually do \frac{r^2 \times \pi \times \Phi}{360} where \Phi is the angle in degrees. Can someone please explain slowly how to transfer from one to the other?
    A = \frac{1}{2} \times r^2 \times \theta
    where \theta is in radians. You want to use an angle in degrees, so you must convert from \Phi degrees to radians:
    A = \frac{1}{2} \times r^2 \times \left ( \Phi \cdot \frac{\pi}{180^o} \right )

    A = \frac{1}{2} \times r^2 \times \left ( \Phi \cdot \frac{2\pi}{360^o} \right )

    and the 2 in the parenthesis cancels the (1/2) out front leaving
    A = r^2 \times \left ( \Phi \cdot \frac{\pi}{360^o} \right )

    -Dan
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member DivideBy0's Avatar
    Joined
    Mar 2007
    From
    Melbourne, Australia
    Posts
    432
    Thanks!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] sec (-1/2) in radians?
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: August 26th 2011, 02:11 PM
  2. Radians help
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: March 23rd 2011, 01:51 AM
  3. radians
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: December 30th 2008, 06:27 AM
  4. Radians :) help please!
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: April 9th 2008, 08:59 AM
  5. Radians
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: February 21st 2008, 04:37 PM

Search Tags


/mathhelpforum @mathhelpforum