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Related rates

  1. Jul 22, 2009 #1
    1. The problem statement, all variables and given/known data

    img001-1.jpg


    i can't think of any equation to plug the 45 degrees angle pls help.... i tried

    Dttanθ=y/x

    (secθ)^2)(dθ/dt)=[x(dy/dt)-y(dx/dt)]/x^2

    but i don't know the value of x when tanθ=45 degrees... do i need to set my calcu to radians or just in degrees mode then i get tanθ=y/x ---> tan45=y/x

    1=y/x
    x=y
     
  2. jcsd
  3. Jul 22, 2009 #2

    nicksauce

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    .
    First, it's θ=45 not tanθ=45. Second, if θ=45 what is the relationship between x and y? Using this relationship and x = 10 + 2t, y = 6 + 4t, can you find x and y when θ=45?

    How about putting it in for that secθ you have in
    (secθ)^2)(dθ/dt)=[x(dy/dt)-y(dx/dt)]/x^2?
     
  4. Jul 22, 2009 #3
    awww sorry hehe mistyped. it's tan45 hehe:uhh:
    i came up with this solution
    x=10+2t
    y=6+4t

    tan45=(6+4t)/(10+2t) (deg mode)
    1=(6+4t)/(10+2t)
    10+2t=6+4t
    t=2

    substituting in (secθ)^2)(dθ/dt)=[x(dy/dt)-y(dx/dt)]/x^2
    i got ((cos45)^2)/7 per sec or 1/14 per sec
    is this correct? or should i set my calculator in radian mode?
     
  5. Jul 22, 2009 #4

    HallsofIvy

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    d(sin x)/dx = cos x and d(cos x)/dx= -sin x ONLY if x is in radians. Those formulas are not valid if the angle is not in radians.
     
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