So, when you go to polar coordinates, basically all you have to remember on the side of integrate is that x becomes r cosine theta. y becomes r sine theta.

在极坐标系里，要记住在积分一侧,只是把x变成rcosθ，y变成rsinθ

youdao

But, basically you don't really need to remember these formulas as long as you remember how to express r in terms of rho sine phi, and x equals r cos theta.

事实上你不用记住这些公式,只需要知道r=ρ*sinφ,而x=r*cosθ

youdao

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

耶鲁公开课 - 基础物理课程节选

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

耶鲁公开课 - 基础物理课程节选

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

耶鲁公开课 - 基础物理课程节选