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Time derivatives of sin and cos phi

  1. Feb 4, 2015 #1
    1. The problem statement, all variables and given/known data
    By using chain rule of differentiation, show that:
    $$ \frac{\mathrm{d} sin\phi }{\mathrm{d} t} = \dot{\phi} cos\phi , \frac{\mathrm{d} cos\phi }{\mathrm{d} t} = -\dot{\phi} sin\phi , $$

    2. Relevant equations


    3. The attempt at a solution
    I got this right for a homework problem, but I'm still confused about why the ##\dot{\phi}## comes out. Does the ##\phi## come out because we are doing:
    $$ \frac{\mathrm{d} sin \phi }{\mathrm{d} \phi} \frac{\mathrm{d} \phi }{\mathrm{d} t} $$

    Also, when do you know if you're working with cartesian unit vectors or ##r## and ##\phi## unit vectors..?
    They have nothing to do with time derivatives right?
     
  2. jcsd
  3. Feb 4, 2015 #2

    Dick

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    Science Advisor
    Homework Helper

    Well, yes. ##\dot{\phi}## means the same thing as ##\frac{\mathrm{d} \phi }{\mathrm{d} t}##. It doesn't really matter what the symbols mean. 'Dot' just usually means 'time derivative'.
     
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