Results 1 to 3 of 3

Math Help - Algebraic Solution OF Sine Equations

  1. #1
    Member
    Joined
    Jan 2007
    Posts
    162

    Algebraic Solution OF Sine Equations

    Solve algebraically the equation
    sin2x + sinx = 0 "0<= x <=360"
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,904
    Thanks
    765
    Hello, r_maths!

    Solve algebraically: . \sin2x + \sin x \:= \:0,\quad 0^o \leq x \leq 360^o

    Double-angle Identity: . \sin2\theta \:=\:2\sin\theta\cos\theta


    Our equation becomes: . 2\sin x\cos x + \sin x \:=\:0

    . . . . . . . . . . . Factor: . . \sin x(2\cos x + 1)\:=\:0


    And we have two equations to solve:

    . . \sin x\:=\:0\quad\Rightarrow\quad\boxed{x \:=\:0^o,\,180^o,\,360^o}

    . . 2\cos x + 1 \:=\:0\quad\Rightarrow\quad\cos x \:=\:\text{-}\frac{1}{2}\quad\Rightarrow\quad\boxed{x \:=\:120^o,\,240^o}

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jan 2007
    Posts
    162
    man, you guys are amazing.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: October 1st 2010, 03:57 PM
  2. Replies: 1
    Last Post: March 24th 2010, 01:14 AM
  3. Sine/Cosine Equations
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: February 21st 2009, 02:17 AM
  4. Algebraic solution
    Posted in the Geometry Forum
    Replies: 1
    Last Post: November 25th 2008, 10:19 AM
  5. Some sine equations
    Posted in the Trigonometry Forum
    Replies: 11
    Last Post: September 2nd 2007, 12:26 PM

Search Tags


/mathhelpforum @mathhelpforum