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Cos,Tan,Sin equations

  1. Jun 20, 2010 #1
    1. The problem statement, all variables and given/known data

    Please help solve these two equations (giving two solutions)

    sin x =√ 2 cos x

    sin^2 x - cos^2 x - 2sin x = 1


    Any help no matter how little is much appreciated





    2. Relevant equations



    3. The attempt at a solution

    Not sure how to solve these,

    thanks in advance
     
  2. jcsd
  3. Jun 20, 2010 #2

    danago

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    Gold Member

    When solving these types of equations, one method is to try and use trigonometric identities to manupulate the equations so that only one type of trigonometric function is left.

    For example, with the first one, what could you divide both sides by so that there is only sin, cos or tan left over?
     
  4. Jun 20, 2010 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    [tex]\frac{sin x}{cos x}= tan x= \sqrt{2}[/tex]
    Can you solve that?

    Since [itex]sin^2 x+ cos^2 x= 1[/itex], [itex]cos^2 x= 1- sin^2 x[/itex] so this becomes
    [tex]sin^2 x- (1- sin^2 x)- 2 sin x= sin^2 x- 1+ sin^2 x- 2sin x= 1[/tex]
    [tex]2sin^2 x- 2sin x- 2= 0[/tex]
    [tex]sin^2 x- sin x- 1= 0[/tex]

    Let y= sin x so the equation becomes [itex]y^2- y- 1= 0[/itex].


     
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