 Hi, I'm Zor. Welcome to Unisor Education. The purpose of this lecture is to explain how cotangent function behaves for basic angles, basic like 30 degrees, 45 degrees, etc. Now, we have examined sine and cosine, and these are major tools because I'm going to do it this way. I will use this definition of cotangent and the fact that I know the values of cosine and sine for all these basic angles, and that's how I will derive the values of the cotangent. Instead of considering this unit circle and triangles, etc., this is easier. So let me just draw a little table which has all the major angles, 0, pi over 6, pi over 4, pi over 3, pi over 2, which is 0 degrees, 30, 45, 60, and 90, and I know my cosine and I know my sine in these cases. So what are they? Well, let's recall cosine at 0 is 1, then at 30 degrees it's square root of 3 over 2, square root of 2 over 2, 1 half and 0. Now, sine is basically the reverse and 1. So what are the values of my cotangent? Well, let's divide one by another. In this case, it does not exist because denominator is equal to 0. This is square root of 3. This is 1. This is 1 over square root of 3, which is square root of 3 over 3. If I multiply by square root of 3 both numerator and denominator, this is a more traditional recording and this is 0. Well, that's it. No big deal. Now, you also know that cosine is an even function and sine is odd function, which makes cotangent an odd function, right? This doesn't change the sine if you change an argument sine and this does. So obviously the fraction, the ratio, would change the sine. Now, that makes actually very easy to calculate something like what's the cotangent of minus 60? Well, that's minus cotangent and 60 and stuff like this. Also, don't forget that cotangent is a periodic function and pi is a period. So you can add pi or subtract pi to any of these values to get other values. So what I'm saying is that all the basic angles around the circle, 30, 45, 90, whatever, 135, 120, all these angles can be derived from these and pi is 180 degrees. And using this manipulation and using the periodicity and the fact that the function is odd, you can derive any other values. So as you see, it's very simple. It's a very short lecture. I just wanted to cover these very basic topics. Now, I'm not sure you have to remember it. The only thing which you do have to remember is probably that the sine of 30 degrees is equal to 1 half. Everything else is kind of easily derivable from just thinking about this triangle. But it's a 45 degrees. It's obviously equal. And it's part of the square and all these little things. Everything is derivable. I mean, you don't have to remember anything. And by the way, one of the purposes of the whole course is that math has internal logic in itself. And not too many things you have to really memorize. Most of these things can be derived. And if you remember how to derive it, which is much easier, at least for me, to memorize certain just numbers or properties, whatever, that would make, actually, it's much more useful knowledge for you. Well, that's it for today. Thank you very much. And I will continue talking about second and co-second in the next lectures. Thank you.