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What's the difference between sin^2(x) and sin(x^2)?

  1. Jan 25, 2012 #1
    1. The problem statement, all variables and given/known data

    what's the difference between sin^2(x) and sin(x^2)?


    2. Relevant equations



    3. The attempt at a solution

    I can't do sin^2(x) on the calculator. let's just use sin(25) as an example, what's the difference?
     
  2. jcsd
  3. Jan 25, 2012 #2

    jedishrfu

    Staff: Mentor

    first expression is sin(x) times sin(x) so you'd enter it as ( sin(x) ) ^ 2 and your calculator should be able to evaluate it.
     
  4. Jan 25, 2012 #3
    [itex]sin^{2}x = sinxsinx [/itex]
    The other 1 is just squaring the x not the whole function.


    Also on a side note,
    [itex]sinx+sinx = 2sinx[/itex]
     
  5. Jan 25, 2012 #4

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Indeed. if x = 5, sin2(x) ≈ 0.919536, whereas sin(x2) ≈ -0.132352
     
  6. Jan 25, 2012 #5

    epenguin

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    Homework Helper
    Gold Member

    sin2x MEANS (sin x)2.

    Which you can calculate on your calculator.

    IMHO you are not the only one and not totally at fault to be confused - sin2x as far as I can see is a sort of mathematical slang, not strictly logical (so no wonder your calculator doesn't understand it either) which by its antiquity is let through and is universal - so there it is to get used to.
     
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