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They always find a new angle, a different part to keen on especially this class. I think they are really keen on.
他们总能找全新的角度，和兴趣点,尤其是这个班级，我认为他们很有热情。
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you know, make you look at things from a different angle.
这会让你从不同的视角看待事情。
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Sorry, said that wrong, p1 radius 1 and angle 2, 2 radians is a little bit more than pi half.
而是半径和角度的表示，在这个例子中点，并不对应这个点,它实际上对应的是。
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You can imagine that if a vector is viewed from an angle, then its components will vary with the perspective.
你可以想象一下,如果换一个角度观察矢量,其分量会相应地发生变化
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And then further you put some recording device, which in those days was a photographic plate, far across a room. So you take a tiny, tiny angle and you go far enough across the room.
接着放一些记录设备，那时用的是一个摄影用的感光片，取一个极小极小的角度,然后去到房间中足够远的地方。
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They want to get as far away from each other possible, the ideal angle is 120. But what we have here is a four-membered ring, so what angle does 90° that have to be, that bond? 90 degrees.
它们想要尽量远离彼此，最理想的是形成120°键角,但现在是个四元环,所以这键角应该多大？
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Now take these two fingers-- the middle finger and the thumb-- and as much as possible, from that 90 degree angle, create a circle.
再让这两个手指-,中指和姆指-,尽可能保持直角时围成一个圆圈。
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And modernism is all about verticality,from a certain angle.
现代主义是从固定角度来看是直立的。
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If its in Cartesian form I'll pass in an x and y and compute what a radius and angle is.
来得到的这个点,我都可以得到这个点的,全部的这种信息。
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The angle is increasing at a steady rate, so we know it's going at a steady speed.
转过的角度以恒定速率增加,所以我们知道它以一个恒定的速度运动
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Another way to represent a point in a plane is I've got a radius and I've got an angle from the x-axis, right, and that's a standard thing you might do.
平面上面的点的方法,也就是极坐标,上面那种方法其实是，如果你们喜欢我这么说的话,笛卡尔坐标表示法。
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And then he just takes that narrow column of light and he admits it to a prism. And what the prism does is takes a tiny, tiny difference in wavelength and refracts it through a different angle.
他只取了那个窄光柱,然后把它对准一个棱镜，棱镜所做的就是,测量出波长的细微差别,然后从不同的角度测定它的折射度。
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self y Notice what I also do here, I create self dot y, give it a value, and then, oh cool, I can also set up what's the radius and angle for this point, by just doing a little bit of work.
我创建了，然后给它赋值，然后，噢太酷了，通过做一点额外的工作,就可以得到点的半径和角度了，好，实际上如果。
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It's now got a different radius, same angle, so I just changed the radius of it.
我刚刚改变了它的半径，噢，但是对于笛卡尔形式来说。
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So, we've achieved the angle that we observed, which is a 109 . 5.
我们得到了我们观察到的角度，是109。5。
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So what we're predicting is a bond angle of 90 degrees.
垂直的轨道上。
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We'll adapt the convention that we'll measure angle in a radian.
我们要适应它,以后都用弧度来表示角的大小
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Okay. For those who have not seen a radian, it's just another way to measure angle with the understanding that a full circle, which we used to think is 360 degrees, So a radian is roughly 60 degrees.
我想告诉那些还不懂弧度制的同学,这是衡量角度的另一种方法,理解起来是这样的,对于一个整圆,也就是我们之前所说的360°,所以1弧度大约是60°
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Ok So, according to this model, 90° what we're seeing is a bond angle of 90 degrees.
我听到不同的答案，OK，，I，hear，a，mix。,根据这个模型，我们看到键角是。
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And just to give you a sense, if you do a cross-cut of this, you cannot show it from this angle, but it should really be sort of a dumbbell shape with the nodal plane in between the two nuclei.
告诉你们这些就是给你们点概念，假如你们把他横切切开，不能从角度上展示，但它还是会保留几分哑铃的形态,以及在两核之间的节面。
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So this is giving me now that template, better way of saying it, all right, a template now, for a point is x, y, radius, angle.
其他的方法来进行计算，但是这就是典型的我，要放置它们的地方，因此这就给了我一个模板。
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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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So we have if, and that is followed by, I'm going to use angle braces here just to indicates something goes in here, some test followed by a colon.
那么我写了if，后面跟着，我这里会用一个角括号,来代表这里有些东西，冒号后面跟着一些测试。
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If it's in polar form I passed in a radius and angle and I'll compute what the x- and y- value is.
以及半径和角度,但是现在是这样的,不管我是以哪种形式。
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So we do, in fact, have a dependence on what the angle is of the electron as we define it in the orbital.
实际上当我们定义电子在这个轨道,它的波函数的确是和角度有关的。
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May hurt a little bit, but try as much as possible to create a 90 degree angle.
可能有点痛，尽可能形成一个直角。
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A magnitude is how long this guy is and direction is at what angle it is.
大小是指它的长度,而方向是指它与坐标轴的夹角
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This says, if you want to be in the air for a long time, so you may think that 90 degrees is the best angle.
也就是说,如果你想在空中停留更久,你也许会认为 90°是最佳选择
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So, in a settling, what is the bond angle here?
这里的键角是多少？
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