Then you're supposed to know derivatives of simple functions like sines and cosines.
你应该知道一些简单函数的导数,比如正弦函数和余弦函数
sine and cosine are definite numbers.
正弦和余弦都是有限大小的数
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
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
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
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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