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I need help on identities

  1. Mar 18, 2007 #1
    Can someone kindly help to find the exact values of cosx and sinx when tanx=2..:redface:
     
  2. jcsd
  3. Mar 18, 2007 #2

    Moonbear

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    Please show your own work on the problem so far so that the homework helpers know where to begin with helping you on this.
     
  4. Mar 18, 2007 #3
    well i could have done it easily if it was in half angle form..i.e tan(1/2x)=2...i have some formulae to use but for that one i have no idea how to start
     
  5. Mar 18, 2007 #4

    robphy

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    In what kind of problem might the expression tan x=2 occur?
     
  6. Mar 18, 2007 #5

    cristo

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    You don't really need a formula as such. Try drawing a diagram (i.e. a right angled triangle). You know the value of the tangent of one angle, so you should be able to write down the values of two of the sides. There's a theorem that you know to find the third side-- try using this.
     
  7. Mar 18, 2007 #6

    arildno

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    Well, the simplest way is to utilize the identity:
    [tex]\tan^{2}(x)+1=\frac{1}{\cos^{2}(x)}[/tex]
    If you are not familiar with that result, you should try to prove it first.
     
  8. Mar 18, 2007 #7

    Hootenanny

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    You don't need any identities to solve the system. Start by finding x...
     
  9. Mar 18, 2007 #8
    Very much appreciated...I used SOHCAHTOA and got the answer I was looking for:smile:
     
  10. Mar 18, 2007 #9

    HallsofIvy

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    Yes, Cristo's answer was the simplest method.

    (Darn, he got it in ahead of me!)
     
  11. Mar 18, 2007 #10

    robphy

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    Ideally, the OP would have used my hint.
     
  12. Mar 19, 2007 #11

    HallsofIvy

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    I understand your point, but I can think of many problems involving tan x= 2 (or other values of tan x) that have nothing to do with right triangles.
     
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