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Intersection of trig F(x)

  1. Apr 11, 2004 #1
    how do i find intersection of sin(x) and cos(x)? wat method do i use?
     
  2. jcsd
  3. Apr 11, 2004 #2
    sinx = cosx
    sinx/cosx = 1
    tanx = 1
    x = arctan(1)
    x = pi/4

    cookiemonster
     
  4. Apr 11, 2004 #3
    Apart from it u can do it graphically. But Still u have to do wat cookie monster( :redface: ) has done
     
  5. Apr 11, 2004 #4
    but wat if is sin(x) and cos(2x) ?
     
  6. Apr 11, 2004 #5
    That's a little more difficult. You'd have to use a half-angle formula and solve it similarly.

    cookiemonster
     
  7. Apr 11, 2004 #6
    with ur help it seems to be

    [tex]sin(x)= 1- 2sin(x)^2[/tex]

    [tex]2sin(x)^2+sin(x)-1=0[/tex]

    hey it works thx all
     
  8. Apr 11, 2004 #7
    wait but how do i solve 2sin(x)^2=tan(x)
     
  9. Apr 11, 2004 #8
    Use the identity:
    [tex]\tan ^2 x + 1 = \frac{1}{\sin ^2 x}[/tex]
     
  10. Apr 11, 2004 #9
    omg i dont reallyget how this identity could help me~
     
  11. Apr 11, 2004 #10
    Eliminate the sin^2(x) with that identity.

    cookiemonster
     
  12. Apr 11, 2004 #11
    That identity should give you:

    [tex]4\sin ^6 x + \sin ^2 x - 1 = 0[/tex]

    Now let t = sin2x and solve the equation.

    (I eliminated tanx rather than sinx.)
     
  13. Apr 11, 2004 #12
    yeah but it trun out to be tan(x)^3+tan(x)-2=0
     
  14. Apr 11, 2004 #13
    So now you gotta do some more factoring. More fun algebra!

    Edit: Fine!

    cookiemonster
     
    Last edited: Apr 11, 2004
  15. Apr 11, 2004 #14
    I think it's -2...
     
  16. Apr 11, 2004 #15
    god i m having a headache with everything
     
  17. Apr 11, 2004 #16
    thx all , i do this after i wake up tommor
     
  18. Apr 11, 2004 #17
    wait tan^2+1= 1/cos^2 is it?
     
  19. Apr 11, 2004 #18
    No, [itex]\tan ^2 x + 1 = \frac{1}{\sin ^2 x}[/itex].
     
  20. Apr 11, 2004 #19

    matt grime

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    Science Advisor
    Homework Helper

    Chen, you might want to check that, as tan of 0 is not infinity.
     
  21. Apr 11, 2004 #20
    Of course you are right.

    [tex]\tan ^2 x + 1 = \frac{1}{\cos ^2 x}[/tex]
     
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