Results 1 to 11 of 11

Math Help - Trouble finding reference angles with radians

  1. #1
    Newbie
    Joined
    Apr 2013
    From
    NYC
    Posts
    8
    Thanks
    1

    Trouble finding reference angles with radians

    I am having trouble finding reference angles with radians. For instance: #1) 33pi/4
    #2) -23pi/6
    How do I go about solving these?
    Last edited by davecolombia; April 13th 2013 at 05:14 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,383
    Thanks
    1474
    Awards
    1

    Re: Trouble finding reference angles with radians

    Quote Originally Posted by davecolombia View Post
    I am having trouble finding reference angles with radians. For instance: 33pi/4 -23pi/6 How do I go about solving these?

    Please do not be insulted by this remark: often it is a problem in basic arithmetic.

    \frac{33\pi}{4}-\frac{23\pi}{6}=\frac{99\pi}{12}-\frac{46\pi}{12}=\frac{53\pi}{12}=4\pi+\frac{5\pi}  {12}.

    Now we can disregard all even multiples of 2\pi.

    Thus in this case we endup with \frac{5\pi}{12}.

    What is the reference angle there?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2013
    From
    NYC
    Posts
    8
    Thanks
    1

    Re: Trouble finding reference angles with radians

    I apologize, I have written them wrong...they are separate questions: #1. 33pi/4 #2. -23pi/6
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Apr 2013
    From
    NYC
    Posts
    8
    Thanks
    1

    Re: Trouble finding reference angles with radians

    I apologize, I have written them wrong...they are separate questions: #1. 33pi/4 #2. -23pi/6
    Last edited by davecolombia; April 13th 2013 at 06:10 PM. Reason: delete
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,383
    Thanks
    1474
    Awards
    1

    Re: Trouble finding reference angles with radians

    Quote Originally Posted by davecolombia View Post
    I apologize, I have written them wrong...they are separate questions: #1. 33pi/4 #2. -23pi/6
    The fact that your post is mistaken makes no difference.
    We can disregard any multiple of 2\pi

    Here is an example.
    \frac{76\pi}{5}=15\pi+\frac{\pi}{5}=14\pi+\frac{6 \pi}{5}.

    So disregard the 14\pi and get the equivalent number of \frac{6\pi}{5} .

    Now what is the reference angle angle?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Apr 2013
    From
    NYC
    Posts
    8
    Thanks
    1

    Re: Trouble finding reference angles with radians

    4pi/5 ?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor

    Joined
    Apr 2005
    Posts
    14,973
    Thanks
    1121

    Re: Trouble finding reference angles with radians

    How did you get that?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Newbie
    Joined
    Apr 2013
    From
    NYC
    Posts
    8
    Thanks
    1

    Re: Trouble finding reference angles with radians

    pi-pi/5=4pi/5
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    Apr 2013
    From
    NYC
    Posts
    8
    Thanks
    1

    Re: Trouble finding reference angles with radians

    whoaa, wait..it is pi/5 which is 36 degrees ... right ?
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Newbie
    Joined
    Apr 2013
    From
    NYC
    Posts
    8
    Thanks
    1

    Re: Trouble finding reference angles with radians

    5pi/12, which is 75 degrees
    Follow Math Help Forum on Facebook and Google+

  11. #11
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,383
    Thanks
    1474
    Awards
    1

    Re: Trouble finding reference angles with radians

    Quote Originally Posted by davecolombia View Post
    5pi/12, which is 75 degrees
    Here are the rules for reference angles.
    First reduce to 0\le \theta <2\pi.

    The the reference angle is \rho where
    If 0<\theta<\tfrac{\pi}{2} then \rho=\theta

    If \tfrac{\pi}{2}<\theta<\pi then \rho=\pi-\theta

    If \pi<\theta<\tfrac{3\pi}{2} then \rho=\theta-\pi

    If \tfrac{3\pi}{2}<\theta<2\pi then \rho=2\pi-\theta.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. A little help with reference angles.
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: January 24th 2010, 09:40 PM
  2. Using Reference Angles
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: April 5th 2009, 02:59 PM
  3. Reference Angles?
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: January 19th 2009, 10:19 AM
  4. Reference Angles...
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: August 15th 2008, 11:56 PM
  5. reference angles
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: May 7th 2008, 06:47 AM

Search Tags


/mathhelpforum @mathhelpforum