来自《耶鲁大学开放课程：基础物理 第4集 第4集》

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  and that's where the trigonometric functions come in.
  这就是引入三角函数的目的
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  So, I make a guess, x is cos(t), and you can check
  假设 x(t) = cos(t) 你可以验证
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  if you take two derivatives, it obeys the equation,
  如果求二阶导数 它满足这个方程
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  the second derivative of x is - x itself.
  并且 x 的二阶导数是 - x
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  But do I like this solution
  这个解怎么样呢
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  or is there something not fully satisfactory? Yes?
  或者说这个解还有什么不足之处吗 你说
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  Pardon me?
  能再说一遍吗
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  Oh, it will be negative x.
  它会变成 - x
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  So, let's do that.
  让我们试一下
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  So let's take dx/dt = -sin(t) .
  取 dx / dt = - sin(t)
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  Then, take one more derivative, d2x over dt2,
  然后再求一次导数 d2x / dt2
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  derivative of sine is cosine.
  正弦的导数是余弦