Results 1 to 3 of 3

Math Help - Trig problem...

  1. #1
    Newbie
    Joined
    Mar 2009
    Posts
    11

    Trig problem...

    I'm stuck on this problem...

    Find all solutions in the interval [0,2π]: 1 - sinx = 2 cos^2x

    any help would be appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,873
    Thanks
    656
    Quote Originally Posted by adam456006 View Post
    I'm stuck on this problem...

    Find all solutions in the interval [0,2π]: 1 - sinx = 2 cos^2x

    any help would be appreciated.
    2\cos^2{x} = 2(1 - \sin^2{x})

    sub that into the original equation for 2\cos^2{x} and solve the resulting quadratic in \sin{x}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1

    Trig equation

    Hello adam456006
    Quote Originally Posted by adam456006 View Post
    I'm stuck on this problem...

    Find all solutions in the interval [0,2π]: 1 - sinx = 2 cos^2x

    any help would be appreciated.
    Use the identity \cos^2x = 1-\sin^2x and then re-arrange as a quadratic in \sin x:

    1 - \sin x = 2(1-\sin^2x)

    \Rightarrow 2\sin^2 x -\sin x -1 = 0

    \Rightarrow (\sin x - 1)(2\sin x +1) = 0

    \Rightarrow \sin x = 1 or \sin x = -\tfrac{1}{2}

    I'll leave these to you.

    Grandad
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Trig word problem - solving a trig equation.
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: March 14th 2011, 07:07 AM
  2. Replies: 3
    Last Post: January 2nd 2011, 08:20 PM
  3. trig problem
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: May 13th 2009, 06:28 PM
  4. trig problem
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: December 10th 2008, 04:23 AM
  5. trig problem
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: April 1st 2008, 02:16 AM

Search Tags


/mathhelpforum @mathhelpforum