Re: [微分] 切線斜率--極座標

[LuisSantos ( )]

※ 引述《ht15trep (柏林=Boring)》之銘言：
:   r = 4sin3θ
:   slope of tangent line at θ=π/4 is ??
:   請問這要怎麼算= =??
:   ans: 1/2


x = rcosθ = (4)(sin3θ)(cosθ)

y = rsinθ = (4)(sin3θ)(sinθ)

   dy |
  ----|
   dx |θ=π/4

   dy/dθ|
= -------|
   dx/dθ|θ=π/4

  (12)(cos3θ)(sinθ) + (4)(sin3θ)(cosθ)|
= ----------------------------------------|
  (12)(cos3θ)(sinθ) - (4)(sin3θ)(sinθ)|θ=π/4

         -1      1          1      1
    (12)(----)(----) + (4)(----)(----)
         √2   √2         √2   √2
= ---------------------------------------
         -1     1            1     1
    (12)(----)(----) - (4)(----)(----)
         √2   √2         √2   √2

   (12)*(-1/2) + (4)*(1/2)
= --------------------------
   (12)*(-1/2) - (4)*(1/2)

   -6 + 2            -4          1
= ---------    =    ----    =   ---
   -6 - 2            -8          2




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