 Now let's look at the effect of different angles on our calculation of work. You remember for a constant force, we calculated the work by multiplying the magnitudes of the force and displacement vectors, and then the cosine of theta, where theta was the angle between the force and the displacement. So our basic example here, I've got a block and it slides horizontally three meters along the desktop to the right. And it's got a force of 10 Newtons directed 25 degrees above the horizontal. When I plug all that into my basic equation, I find that I've got 27.2 Newton meters. We're going to compare some other values to that. So what if I had a negative angle instead? So rather than pulling up above the horizontal, I'm pulling slightly down below the horizontal. Well, if I plug that into my equation with the negative 25 in there, I still get the same value of 27.2 Newton meters. And that's because, in general, the cosine of minus 25 equals the cosine of 25 because cosine is a symmetric function. Any time you have a negative angle, you get the same value as if you had the positive angle. So let's look at a few other special angles. So if I have a parallel force and displacement, that means the angle between them is 0 degrees. The cosine of 0 is a value of 1. It's one of our special values for the angle. So when I plug that all in, I end up with 30 Newton meters. Just like I multiplied the force and the displacement and didn't worry about the angle. But instead of thinking about it as not worrying about the angle, it really is a cosine of 0 degrees. I just get the full amount of work done here if the force and the displacement are parallel to each other. What if it's perpendicular? Well, if I've got perpendicular forces, that means I really have an angle of 90 degrees. And so the cosine of 90 is 0. So when I plug in my cosine of 90, I find that I get 0 Newton meters. Now this is really the case where this force is not contributing to that displacement at all. So it is not contributing any work. It's not transferring any energy. So we can move around just a little bit more and look at obtuse angles. In this case, I've got 145 degrees for my theta. If I plug that in, what I find is I've now got a negative value for the work. So you can think of it as this force is partially resisting this motion. The motion is going forward. But the force is pulling back a little bit. So I get negative values when I have obtuse angles. The most extreme obtuse angle would be if it's completely reversed or an angle of 180 degrees. Well, the cosine of 180 is minus 1. So when I plug this all in, I get minus 30 Newton meters. So that's the maximum negative work I could possibly have in this particular situation. So to summarize, when our force and our displacement are in the same direction, you've got the largest positive work. When I've got them at 180, that's my largest negative work. Any acute angle gives me positive work. And any obtuse angle gives me negative work. And I've got no work if I'm at an angle of 90 degrees. So now as you approach different problems, you can think conceptually about what type of work you expect to get and how that angle effect is going to affect your work.