 In two previous videos I have shown you what you do if you have uncertainties in measurements and then have to do some calculations based on those measurements. There is a video, what you do if you have additional subtraction and another one what you do if you have multiplication and division. The links of those videos should be somewhere below in the description. Now the question however is what do we do if it gets more complicated? What do I mean by more complicated? For example if you have a vector of length A at an angle theta and your length of the vector has an uncertainty as well as the angle and what you want to do is figure out the Y component of the vector. So AY of course is A times sine of the angle. So I have multiplication but on top of that I have the sine of division. So what do we do? We use the minmax method. The minmax method you already know it from estimating uncertainties where we used it. Also the link to that video should be somewhere below in the description. We take the best possible value to that we add and subtract the uncertainty of the maximum possible outcome minus the minimum possible outcome divided by 2. So in my case my AY best is simply 5 newtons times sine of 30 degrees. I just realized there was a mistake here of course the angle is measured in degrees and not in newtons which gives me 2.5 newtons. So I know the Y component the best case is 2.5 newton and now the main question is plus minus how much. So what do I do? I look at all possible combinations. So in my case what is the biggest angle? What is the smallest angle? What is the biggest amplitude? And what is the smallest amplitude? And then I make a little square here and then write my highest angle that was 40 degrees. My lowest angle 30 minus 10 is 20 degrees. My biggest amplitude 5 plus 1 is 6 newtons. My smallest amplitude is 5 is 4 newtons and then I'm calculating all possible combinations of this. So in this field I'm doing 6 newtons and sine of 40. In this field I'm doing 6 newtons and sine of 20. Here I will do 4 newtons times sine of 40 and here I will do 4 newtons times sine of 20. So let's calculate this. So I have 4 newtons and this I have a maximum possible outcome of 3.9 and for my smallest angle I have 4.1 for this one here I got 2.6 and over here 1.4. So now once I've done this I'll have to look in my values which one is my highest which is this in this case and which one is my smallest which is this in this case and plot it in here. So I have plus minus 3.9 minus 1.4 divided by 2. Now if I calculate this this gave me 1.2 newtons. So as those of you that have watched many of my videos yet I like to round this to one significant figure so I'm going to report this with one significant figure on Newton of uncertainty and my Y component round it so that only one estimated digit is 3 newtons plus minus 1 newton and this is my final answer.