 Hi, I'm Zor. Welcome to a new Zor education. This is the last short lecture about trigonometric function, taking certain values for basic values of argument, basic angles. So, today we'll talk about cosecant and angles which I'm talking about are 0, pi over 6, pi over 4, pi over 3, pi over 2. Now, the most important tool which I'm using is the definition of the cosecant of x, which is 1 over sin. So, if I know the sin, I will just invert it, and that's how I will get the values for these angles, right? So, if this is my sin, sin of 0 is 0, sin of pi over 6, which is 30 degrees, is 1 half, pi over 4, which is 45 degrees, that's square root of 2 or 2. Now, this is 60 degrees, this is square root of 3 over 2, and this is 90 degrees, which is 1. So, knowing that, what is the value of 1 over sin for these angles? So, the cosecant takes value of, doesn't exist in this particular case, because it's invert. This is 2, this is 2 over square root of 2, which is square root of 2. This is 2 over square root of 3, which is 2 square root of 3 over 2, over 3, sorry, and this is 1. Now, sin is an odd function that makes cosecant odd function as well. So, knowing these values, you can always calculate what's the values for corresponding negative angles. It will be just negative these values. Also, you know that cosecant is a periodic function since sin is a periodic function and the period is 2 pi, so you can add 2 pi, subtract 2 pi, and also you know that this property of sin, so if you add pi 180 degree, you will invert the sin, which is an ordinate of an angle. So, that actually makes exactly the same rule for cosecant. So, cosecant of x plus pi also will be equal to... So, this plus the fact that it's odd and periodic function is sufficient to get the value of the function for any nice angle, like 270 degree, for instance, around the unit circle. Very short lecture. Again, it's just as a reference material. You don't have to remember this. Everything is derivable. That's what's very important. You can derive the value from the sin and even sin for major angle. You don't really have to remember because you can always derive it using the triangles. It's either 30, 60 triangle or 45, 45 right triangle. That's it for today, another small lecture, and then I will concentrate on the more important properties to trigonometric functions. Thank you very much.