You've got to know your trigonometry, you've got to know what's a sine and what's a cosine.

你们得懂三角学,你们得知道什么是正弦什么是余弦

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Then they started the cosine tape.

但是他们花了很长的时间来尝试着。

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sine and cosine are definite numbers.

正弦和余弦都是有限大小的数

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I'm using the fact that when you take a cosine and change the angle inside the cosine, it doesn't care. whereas, if you go to the sine and change the angle inside the sine, it becomes minus sine.

我用了一个结论,当你使用余弦函数时,改变角度的正负,函数值不变,而对于正弦函数,改变角度的符号,则函数值也会变号

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But since sine square plus cosine square is 1, you'll find this vector has a fixed length R.

但是由于正弦和余弦的平方和为1,你会发现这个矢量模长恒等于 R

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I'm going to just put that in, and it's the cosine of the number times i plus sine of the number times j times R.

我要在式子加入这个量,这个式子就等于这个值的余弦乘以 i,加上这个值的正弦乘以 j 再乘以常数 R

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Once you do that, I think it's fairly clear that it has got a y component that's given by cosine the x component is negative.

用了这个结论,我想很明显,y 分量由 cos φ 给出,它的 x 分量是负的

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We know it's going around in a circle because if I find the length of this vector, which is the x-square part, plus the y-square part, I just get r square at all times, because sine square plus cosine square is one.

我们之所以知道它做圆周运动,是因为我求出了这个矢量的模长,也就是 x 的平方加上 y 的平方,我就得到了它在任意时刻的模长平方,因为正弦平方加余弦平方始终等于1

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