Results 1 to 2 of 2

Math Help - How do I use reference angles to find these answers?

  1. #1
    Newbie
    Joined
    Dec 2008
    Posts
    1

    How do I use reference angles to find these answers?

    The problem says use reference angle method and gives me this:

    1.) tanx = sq root of 3, 0< x < 4pie

    2.) 2sin^2(x) + cosx = 1, 0< x< 2pie

    I mean, I understand enough of sine and cosine to understand what it's asking, but I don't know exactly the proper steps to find the answer. Any help would be greatly appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,560
    Thanks
    1425
    Quote Originally Posted by I_needhelp View Post
    The problem says use reference angle method and gives me this:

    1.) tanx = sq root of 3, 0< x < 4pie

    2.) 2sin^2(x) + cosx = 1, 0< x< 2pie

    I mean, I understand enough of sine and cosine to understand what it's asking, but I don't know exactly the proper steps to find the answer. Any help would be greatly appreciated.
    1. \tan{x} = \sqrt{3}, 0 < x < 4\pi


    x = \tan^{-1}{\sqrt{3}}

    There will be an answer in the first quadrant, and an answer in the third.

    So x = \{\frac{\pi}{3},\pi + \frac{\pi}{3}\}.

    Also, every iteration of the unit circle will have 2 solutions. This can be represented by adding 2n\pi, where n is an integer.

    So x = \{\frac{\pi}{3}, \frac{4\pi}{3}\} + 2n\pi.

    Letting n equal different values enables you to find all solutions in the domain.

    Let n = 0 you have x = \{\frac{\pi}{3}, \frac{4\pi}{3}\}

    Let n = 1, you have x = \{\frac{7\pi}{3}, \frac{10\pi}{3}\}.

    Any n > 1 has solutions out of the domain.

    So all the solutions are

    x=\{\frac{\pi}{3}, \frac{4\pi}{3}, \frac{7\pi}{3}, \frac{10\pi}{3}\}.
    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