 Here we are now going to describe how the trigonometric ratios differ as you change the angle so It is to be understood in this way that the trigonometric ratios are always dependent on the angle of which the trigonometric ratios are defined for for example in this case if you look closely I am now going to move the point B on the circle So the point B is moving on the circle the constraint on point B is it cannot leave the Circumference of the circle now as I'm moving in the anticlockwise direction. You can see The angle value is increasing Angle value is increasing right now It is 48.2 degrees as I'm increasing now it is going towards 90 degree Simultaneously if you see the perpendicular height if you notice is also increasing right so nine two point nine two now point nine three point nine four like that and The base is also decreasing the value of B So point C is coming closer to a point B is going towards And you know towards the y-axis So this is how it is now I am taking it down So if you see as B is coming down the angle is going towards zero C is coming towards and going to merge with B soon. So this is how it is So you must be familiar with this changing of position of B So as I'm increasing the B from zero towards 90 Hypotenuse length remains the same perpendicular keeps on increasing base keeps on decreasing and then finally base becomes zero over here and as I cross the 90 degree mark and you see now The angle is more than 90 degree. It is in point B is in second quadrant and if you notice We can still find ratios of P by B P by H and all that and on the right hand side If you can see the values are changing So as the theta is increasing the values are now some of the values are also negative If you can see cos theta is negative Than theta is negative Secant theta and cotangent theta are negative Why because in this case B has gone B has become negative because it is a negative x axis Now as I'm going towards the third quadrant again Few ratios are negative views are few are positive Both P and B have become negative now Now as I am crossing the Third quadrant I'm moving into fourth quadrant again few are negative and few are positive So if you notice once again, I'm showing only in first quadrant all the All the ratios are positive. Can you see all the ratios are positive? As the point B moves into the second quadrant See cos theta and tan theta has become negative. Why? Because if you notice point C is in the negative x axis. So base is negative Point B is still in the first in you know the yx The x y coordinate of point B that is this line BC is still positive. So hence Sin is positive right and hypotenuse is always considered to be positive as I move To the sec the third quadrant now both Ac as well as BC has become negative. Can you see? Though it is not being shown here in the diagram, but you can see that C point C here is in negative x axis Similarly, this length BC is also along the negative y axis. So hence both are negative So only tan is positive because negative by negative becomes positive Isn't it? Now as I move the point B again, you can see the base is shrinking perpendicular is Increasing and I in fourth quadrant as I am moving Towards 360 degrees base is increasing again perpendicular is shrinking And cos values are positive all other are negative cos and secant are positive All other are negative. So this is how So you can use this session to understand how Theta changes and basis that how the ratios are also changing. So hence Don't don't think that trigonometry is all about angles lesser than 90 degrees There is significant meaning of Angle more than 30 degrees. Oh, sorry 90 degrees as well. So basically if you now, let me stop here So if you see at 124.2 degrees from the positive x axis The sine value will be defined as nothing but the length of BC, which is positive because it is in the Positive side of the you know y quarter y axis. So b cb is along positive y. So it is positive But ac is negative ac this line ac is negative y because it is along the negative x axis So hence, let us say if you have to find out sine of this value 124.2, which would be nothing but Drop the perpendicular from b which happens to be positive and the foot of the perpendicular that is c Is away from a so how much is this when there's a negative value Then hence sine theta here will be nothing but opposite by hypotenuse, which is 0.83 in the positive direction divided by one Which is the hypotenuse length or the radius of the circle and the value is 0.83 Similarly cos theta will be b by h. So b is in this case. It is negative negative though it is shown here as 0.56 because the absolute value of that Side ac is 0.56 but since it is in the negative direction Hence it is minus 0.56. So hence these are these ratios are for calculation purposes But the actual values are 0.83 minus 0.56 minus 1.47 1.21 minus 1.78 and 0.68 so hence this These are these are the values You can notice how values of the trigonometric ratios are changing as theta is increasing and And from 0 to it has all the the full coverage of 0 to 360 degrees Okay And if it is more than 360 then it starts repeating the value it starts repeating Isn't it see you can see as I'm I'm completing 360 degrees. I'm going now again back to the first quadrant So the values will start repeating. So this is all about the different values of trigonometric ratios at different different angles