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Trigonometric Equations

  1. Jan 8, 2008 #1
    1. The problem statement, all variables and given/known data
    sinx + cosx = 0


    2. Relevant equations
    N/A


    3. The attempt at a solution

    sinx + cosx = 0

    sinx = -cosx
    sinx = (+/-) sqrt(sin^2x - 1)
    (sinx)^2 = (+/-) sqrt(sin^2x - 1)^2
    sinx = sin^2x - 1

    Not really too sure what to do from here on.

    The answer is 3[tex]\pi[/tex]/4 and 7[tex]\pi[/tex]/4.

    I appreciate the help, thanks in advance.
     
  2. jcsd
  3. Jan 8, 2008 #2
    [tex]sin x = -\cos x[/tex]

    Divide by cosx, what identity do you get?
     
  4. Jan 8, 2008 #3

    HallsofIvy

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    Or, since you have gone to all the work of getting to [itex]sin(x)= sin^2(x)- 1[/tex], let y= sin(x) and rewrite it as y^2- y- 1= 0. solve that quadratic equation for y and then solve sin(x)= y.
     
    Last edited: Jan 9, 2008
  5. Jan 8, 2008 #4
    Thank you for the assistance, I can't believe I missed that!
     
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