Results 1 to 7 of 7
Like Tree2Thanks
  • 2 Post By skeeter

Math Help - Solving Trigonometric Equations

  1. #1
    Newbie
    Joined
    Nov 2012
    From
    US
    Posts
    3

    Solving Trigonometric Equations

    Solve the following equation algebraically. Give a general solution.

    3cos2x+cosx=2
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,896
    Thanks
    1755
    Awards
    1

    Re: Solving Trigonometric Equations

    Quote Originally Posted by vanessa81929 View Post
    Solve the following equation algebraically. Give a general solution.
    3cos2x+cosx=2
    Can you solve 3u^2+u-2=0~?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,037
    Thanks
    883

    Re: Solving Trigonometric Equations

    Quote Originally Posted by vanessa81929 View Post
    Solve the following equation algebraically. Give a general solution.

    3cos2x+cosx=2
    3\cos^2{x} + \cos{x} - 2 = 0

    (3\cos{x} - 2)(\cos{x} + 1) = 0

    can you finish?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Nov 2012
    From
    US
    Posts
    3

    Re: Solving Trigonometric Equations

    cosx= 2/3 cosx= -1

    what do you do next?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,037
    Thanks
    883

    Re: Solving Trigonometric Equations

    Quote Originally Posted by vanessa81929 View Post
    cosx= -2/3 cosx= -1

    what do you do next?
    in the interval [0, 2\pi] ...

    \cos{x} = {\color{red}+}\frac{2}{3} ... x = \arccos\left(\frac{2}{3}\right) and x = 2\pi - \arccos\left(\frac{2}{3}\right)

    \cos{x} = -1 ... you tell me what x value on the unit circle has a cosine of -1


    if you want all solutions, add integer multiples of 2\pi to all three solutions.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Nov 2012
    From
    US
    Posts
    3

    Re: Solving Trigonometric Equations

    For the first one, x= 0.841+2npi

    And for the second one, x=pi+2npi

    Where are you getting a third solution from?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,037
    Thanks
    883

    Re: Solving Trigonometric Equations

    \cos{x} = \frac{2}{3} has two solutions, one in quad I and one in quad IV


    for x = \pi, the general solution should be written ...

    x = \pi + 2k\pi , k \in \mathbb{Z}

    ... and put away the calculator.
    Thanks from vanessa81929 and topsquark
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Solving trigonometric equations:
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: August 12th 2011, 11:15 AM
  2. Solving Trigonometric Equations
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: April 18th 2010, 03:45 PM
  3. Solving Trigonometric equations
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: March 23rd 2009, 11:48 AM
  4. Solving trigonometric equations
    Posted in the Trigonometry Forum
    Replies: 0
    Last Post: October 14th 2008, 04:53 PM
  5. Solving trigonometric equations help
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: January 12th 2008, 03:20 PM

Search Tags


/mathhelpforum @mathhelpforum