 So, welcome to this session on trigonometry, today we are going to discuss trigonometric ratios. So, for that we have drawn a circle over here and though the name suggests that it is something to do with triangles but we will be restricting ourselves to the study of a circle and we will see the triangle has to be carved out from that circle and how we will discuss that in a little while. So as the name suggests, trigonometry is nothing but measurement of triangles or basically trigonometry is all about ratios of the three sides of the triangle. So if you know if there are three sides, how many possible ratios are there? So if you see number of possible ratios are six, isn't it? There are six possible ratios if there are three sides and if you see we have named each of these ratios. So for example, sin theta is p by h and cos theta is b by h and so on and so forth but before that let us first understand the nomenclature. So if you see this a, b, c is a triangle, right angle triangle and right angle at a. So here angle c is 90 degrees. Now a, b is the hypotenuse as you can see, b, c is the perpendicular from b and a, c is the base. Now how do, how, why and how I have created the circle is something like this. So let us draw a unit circle. Unit circle means a circle with radius one. So if you see this is the radius one of the circle. I have drawn a circle with a unit radius and after that I have taken any point b, any point b on the circumference. So this point b circumference and from here I have dropped a perpendicular on to the x axis. So if you see this is our x axis, okay. A is at the origin and b is the point on the circumference of the circle and I have dropped a perpendicular on x axis and I have simply joined a and c. So what do we see in a circle if you take a point b and drop a perpendicular on to x axis and this is called foot of the perpendicular, this point c is foot of the perpendicular. So join the center and the foot of the perpendicular you will get a right angle triangle always. Now trigonometry is all about the studies of you know the ratio of the three sides of a triangle so obtained. And we have named all these ratios as well. So if you see sin theta is equal to p by h right what which means perpendicular by hypotenuse. Also if you see if this angle is theta then this this side is opposite angle this is what this is my opposite angle to opposite to theta right and this side is adjacent to theta this side is adjacent to theta isn't it now and this is hypotenuse. So you can remember the ratios in terms of these sides as well. So if you see sin theta is p by h so perpendicular by hypotenuse then cos theta is defined by p by h then tan theta is defined by p by b that is opposite by adjacent cosecant theta is h upon p that is hypotenuse by opposite secant theta is defined as hypotenuse by adjacent and cot theta is defined as b by p ok these are the six trigonometric ratios.