 Hi, this is Chichu. Now, what we're going to do in this table is generate the trig table, the trigonometric ratios table for the special right triangles and the unit circle for the nodes, for the three primary trig ratios, and we're going to take a look at what those angles are in degrees and radians. Okay. Now, we're going to go through this fairly fast. If you're looking for a more detailed explanation of the intricacies, explaining the intricacies of what's in the table, I've put out a video that's fairly long, hour plus 15 minutes or so, going in, going through this table in detail, right? And if you want to sort of a review of what we're about to go through, then there's a shorter video that doesn't have any commentary generating the same table, and that's sort of basically I put together so that you can review just before an exam, or if you want to see how quickly you can generate the table, because what I do tell my students is, when they get their exam to, you know, put their name on the exam, put their exam aside and grab, you know, the scrap paper that they have, and to generate this table as quickly as possible, and this isn't about memorizing this table, because if you're memorizing this table, then you really don't understand the intricacies of what's going on. And you can't appreciate it as much if you're just memorizing it. If you learn how to generate it, then it basically means that you understand the basic concepts of trigonometry, and you can deal with the more complicated problems. Okay. So what I'm going to do to generate this table is I'm going to flip the paper like this, and I'm going to make it as big as possible so it does come out on the camera. And it's okay to do like this if you're writing a test as well, that way everything's big, stands out for you, right? So what we need is our unit circle. The coordinates are 1, 0, 0, 1, negative 1 and 0, 0 and negative 1. We've got two special retriangles, 30 degrees, 60 degrees, 1 squared of 3, and 2. And the other one is 45, 45 and 90, 1, 1, square root of 2, right? What we have now is we're going to generate our rows. Our rows are radians, data and degrees, sine theta, cos theta, and tan theta, right? Let's separate it. Now let's just go down the degrees row. We'll go across the degrees, right? That way we can set up our columns properly. So our degrees we have 0 degrees, 30 degrees, 45, 60, and 90. And then as soon as we hit 90 we come back again, right, as we discussed. 90 plus 30 is 120, plus 45 is 135, 150, and then 180. And then we're going to add 30 to 180. We've got to 10, 45 to 25, to 40, and then to 70. And then we've got 300, 3, 15, 3, 30, and 3, 60. Okay. Now I'm just going to generate the columns so these guys are separated properly. So when we're reading now we're not going to mistakenly read the wrong bit of info. Why does it make this possible, right? As neat as possible. So we've gone across the degrees to generate the radians. And I usually do both degrees first and then generate the radians. I don't do the way we did it for the trig ratios first and then do the radians. So for radians 0, degrees and radians is 0, 180 is pi. And then we're going multiples of pi basically, right? We're going to use pi to generate everything in the first quadrant. And then we're going to use the first quadrant to generate everything in the second, third, and fourth quadrant, right? So 4, 30 degrees, we divide 180 by 6. So we're going to do the same thing with pi, right? So 30 degrees is pi over 6, 45 is pi over 4, 60 is pi over 3, 90 is pi over 2, 120 is multiple of 60, so multiply 3 pi over 3 by 2, so it's 2 pi over 3, 135 is multiples of 45, 1, 2, 3, so 3 pi over 4, 150 is multiples of 30, times 5, so 5 pi over 6. 210, yeah, 210 is 30, so 7 pi over 6, 225 is 1, 2, 3, 4, 5, 5 pi over 4, 240 is 60 times 4, so 4 pi over 3, 270 is 3 pi over 2, 300 is multiple of 60, 5 pi over 3, right? We're always going with the biggest number that gets us to wherever we want to go. Because 30 does, but you would have to reduce 10 pi over 6 to 5 pi over 3, right? 300, 315 is multiples of 45, so we're at 5 pi over 4 here, 6 pi over 4, 7 pi over 4, 7 pi over 4, right? Multiples of 45, 1, 2, 3, 4, 5, 6, 7, 330 is multiples of 30, 11 pi over 6, and 360 is 2 pi, right? Let's try to rewrite the sine row, right? Sine of 0, we're here, it's y, so it's 0, sine of 30 is 1 over 2, sine of 45 is 1 over root 2, and you can rationalize the denominator for this and write it down as root 2 over 2, sine of 60 is root 3 over 2, sine of 90, we're up here, it's y, so it's 1, right? And the rest of this, I'm going to use both my hands, because all I do, I just track, it's symmetry, right? You come here and you go back, so you're going to go root 3 over 2, 1 over root 2, 1 over 2, 0, back again, 1 over 2, 1 over square root of 2, root 3 over 2, 1, back again, root 3 over 2, 1 over root 2, 1 over 2, and 0, okay? Now all we have to think about is where is sine negative, sine is negative, and the second and the third and fourth quadrants, so from 180 to 360, so from 180 to 360, it's negative, because it's y, and y is negative below the x-axis, so fairly quickly, the cos column, well, it's the inverse, the flap of the sine, but I'm going to use these guys, because, well, we can use both, either way, right? cos of 0 degrees, we're over here, it's x, so that's 1, cos of 30 is root 3 over 2, right? cos of 45 is 1 over root 2, and cos of 60 is this guy coming here, 1 over 2, and then 0, right? because we're here, the x is 0, right, and then we're just going to track back again, 1 over 2, 1 over root 2, root 3 over 2, 1, back again, root 3 over 2, 1 over root 2, 1 over 2, 0, back again, 1 over 2, 1 over root 2, root 3 over 2, and 1, now all we have to worry about is where is cos negative, cos is negative on this side of the y-axis, and the second and third quadrants, so from 180 degrees, sorry, from 90 degrees to 270, it's negative, 90 degrees to 270, it's negative, negative, negative, negative, negative, negative, 0 can't be negative. Now, for the tan, I'm going to use the unit circle and the special right triangles for this, and actually, I'm going to use the special right triangles and the fact that tan is sine divided by cos, right? So tan of 0, at the nodes I'm going to use, sine divided by cos, tan of 0 is sine divided by cos, 0 over 1 is 0, tan of 30 degrees is 1 over root 3, and again, you can rationalize the denominator for this, and it becomes root 3 over 3, tan of 45 is 1 over 1, which is 1, tan of 60 is root 3 over 1, which is root 3, and then we're at a node, 1 divided by 0 is undefined, right? Now, all I do again is just track back, so root 3, 1, 1 over, oh my pen is dying, let's switch up the pen, should work, let's see, square root of 3, 1 over, where were we? So we're here, square root of 3 and 0, and always, if you're going to write a test, bring multiple pens, right? And then we're going to go back again, 1 over root 3, 1 square root of 3, undefined, back again, root 3, 1, 1 over root 3, 0, right? And all I have to worry about now is where is tan negative? Tan is sine divided by cos, so over here in the first quadrant, they're both positive, positive over positive is positive, over in the second quadrant, sine is positive, cos is negative, so tan is negative, right? Positive divided by negative is negative. In the third quadrant, we got negative divided by negative, that's positive. In the fourth quadrant, we got negative divided by positive, that's negative, right? Negative, negative, negative, okay? And that's how you generate the special triangles, unit circle, and the trigonometric table, and what we would do is put this on the side and bring back our test and start doing our test, and we're going to end up using this a lot, and when we start doing problems, questions, we're going to refer to this a lot, okay? So keep this thing in mind, because this is extremely handy. Learn how to generate it. Now in the next video, what we're going to do, we're going to generate this without any commentary, as if you would in a test, because you really don't want to speak out, you know, in a test, verbally say everything that you're doing. So we'll generate this really quickly, and you'll see how fast you can do it, okay? I'll see you guys in the next video. Bye for now.