 Hi and welcome to the session. Today we will learn trigonometric ratios of some specific angles. We will learn the trigonometric ratios of 0 degrees, 30 degrees, 45 degrees, 60 degrees and 90 degrees. So for that let's make a table. So let's find out these trigonometric ratios for angle A. When angle A is 0 degrees, 30 degrees, 45 degrees, 60 degrees and 90 degrees. Sign 0 is 0. Sign 30 is 1 by 2. Sign 45 is 1 by root 2. Sign 60 is root 3 by 2. Sign 90 is 1. Now I will tell you a very easy way to make this table. You just need to remember the values of sign A for all these angles. Now to find the values of cos A for these angles, just take these values from right hand side. This we have 1, so we will write 1 over here as cos 0, then root 3 by 2, so write it here. So cos 30 is root 3 by 2, then 1 by root 2. So here we have 1 by root 2 and cos 45 is 1 by root 2, then comes 1 by 2. So cos 60 is 1 by 2 and then 0. So that means cos 90 is 0. Now we need to find the values of tan A for these angles and we know that tan A is sin A over cos A. So tan 0 will be sin 0 over cos 0, that is 0 upon 1, that is 0. Similarly, tan 30 is sin 30 over cos 30. So 1 by 2 upon root 3 by 2 will be 1 upon root 3. Similarly, tan 45 will be 1 upon root 2 upon 1 upon root 2, that will be 1. So tan 60 is root 3 by 2 upon 1 by 2, that is root 3 and tan 90 is 1 upon 0, which is not defined. Now comes cos A and we know that cos A is the reciprocal of sin A, that is 1 upon sin A. So cos 0 will be 1 upon 0, that is not defined. Cos 30 will be the reciprocal of sin 30. So it will be the reciprocal of 1 upon 2, that is 2, cos 45, reciprocal of 1 upon root 2, that is root 2, cos 60 will be reciprocal of root 3 by 2, that is 2 upon root 3 and cos 90 will be 1 upon 1, that is 1. Now we need to find the values for secant A and secant A is the reciprocal of cos A. So secant 0 will be 1 upon 1, that is 1. Secant 30 will be the reciprocal of root 3 by 2, that is 2 by root 3. Secant 45 will be the reciprocal of 1 by root 2, that is root 2. Secant 60 will be the reciprocal of 1 by 2, that is 2 and secant 90 will be the reciprocal of 0, that is 1 upon 0, which is not defined. Lastly we need to find the values of cot A, which is the reciprocal of tan A. So cos 0 will be the reciprocal of tan 0, that is 0. So its reciprocal will be 1 upon 0, which is not defined. Cot 30 will be the reciprocal of 1 by root 3, that is root 3. Cot 45, that is reciprocal of 1, that is 1. Now cot 60 will be the reciprocal of root 3, that is 1 upon root 3 and cot 90 will be the reciprocal of tan 90. Now tan 90 is not defined and not defined is 1 upon 0. So the reciprocal of 1 upon 0 will be 0 upon 1, which will be equal to 0. So cot 90 is 0. Now the value of sin A is always less than or equal to 1. Also the value of cos A is less than equal to 1 and the value of cosecant A is always greater than or equal to 1. Also the value of secant A is always greater than equal to 1. Now let's take one small example for this. Suppose we need to find the value of cos square 30 degrees plus tan square 60 degrees plus cosecant 90 degrees plus sin 0 degrees. So let's see the table, cos 30, cos 30 is equal to root 3 by 2. So this will be root 3 by 2 square plus now we need tan 60 degrees. So tan 60 is root 3. So this will be root 3 square plus cosecant 90, cosecant 90 is 1. So plus 1 plus sin 0, that is 0. So this will be equal to 3 upon 4 plus 3 plus 1 plus 0, that is equal to 19 upon 4. So here we have learnt trigonometric ratios of some specific angles. With this we finish this session. Hope you must have enjoyed it. Goodbye and have a nice day.