Anderson Video - Trigonometry

Professor Anderson
20 views
Was this helpful ?
0
>> Hello class, Professor Anderson here. Let's talk a little bit about triangles. They're going to come back to haunt us again and again in this class, and we really have to understand triangles very well. Okay, so what does a triangle look like? The triangle looks like that. Okay, that is a special kind of triangle called a right triangle, so we put that symbol right there, which means 90 degrees. Now, if we label this theta and we label the sides A, B, C, what do we know about triangles? The Pythagorean theorem, okay. A squared plus B squared equals C squared. Good. What else do we know about triangles? Specifically right triangles? >> Sine, cosine, and tangent. >> Sine, cosine, and tangent, our good old friend. SOHCAHTOA, I won't tell you what I told you earlier about what that means, but you probably all remember. Sine is equal to opposite over hypotenuse. In this case, what is opposite the angle? Well, it's B. Sine theta is opposite over hypotenuse, B over C. Cosine theta is adjacent over hypotenuse. Adjacent means adjacent to the angle. If this is the hypotenuse, this is the only other side that is adjacent to the angle. So we have to have A over C. and then finally, tangent of theta is opposite over adjacent, which would be B over A. Okay? Make sure you understand triangles, and specifically when you start rotating these triangles around, gets a little more complicated. Let's just confirm that we can do this for a different orientation of triangle. So let's say we have a triangle that looks like this. Okay? And now let's label the sides. Let's make up some new ones. How about W, Z, and Q. Okay. Now, what is sine of theta for that triangle? >> Whatever we need it to be. >> Whatever you need it to be, okay? There's a great joke in physics that the answer is 3. It just depends on what units you pick. I know, physics humor, you can't get enough of it. >> We need to know what theta is. >> We need to know where theta is, right? Theta is going to be rather important. So let's say theta is now right there. If that's theta, what is sine of theta? Well, it's opposite, which is opposite the angle, which in this case would be W over hypotenuse, which in this case is Q. Cosine of theta we said was adjacent over hypotenuse. The adjacent side is right here, so that would be Z divided by the hypotenuse which we said was Q. And then finally tangent of theta is going to be opposite W over adjacent Z. Okay? In physics, we're going to end up working with X and Y's, but those are just variables. We can use any variables we want. All right? Hopefully, that is reasonably clear.
>> Hello class, Professor Anderson here. Let's talk a little bit about triangles. They're going to come back to haunt us again and again in this class, and we really have to understand triangles very well. Okay, so what does a triangle look like? The triangle looks like that. Okay, that is a special kind of triangle called a right triangle, so we put that symbol right there, which means 90 degrees. Now, if we label this theta and we label the sides A, B, C, what do we know about triangles? The Pythagorean theorem, okay. A squared plus B squared equals C squared. Good. What else do we know about triangles? Specifically right triangles? >> Sine, cosine, and tangent. >> Sine, cosine, and tangent, our good old friend. SOHCAHTOA, I won't tell you what I told you earlier about what that means, but you probably all remember. Sine is equal to opposite over hypotenuse. In this case, what is opposite the angle? Well, it's B. Sine theta is opposite over hypotenuse, B over C. Cosine theta is adjacent over hypotenuse. Adjacent means adjacent to the angle. If this is the hypotenuse, this is the only other side that is adjacent to the angle. So we have to have A over C. and then finally, tangent of theta is opposite over adjacent, which would be B over A. Okay? Make sure you understand triangles, and specifically when you start rotating these triangles around, gets a little more complicated. Let's just confirm that we can do this for a different orientation of triangle. So let's say we have a triangle that looks like this. Okay? And now let's label the sides. Let's make up some new ones. How about W, Z, and Q. Okay. Now, what is sine of theta for that triangle? >> Whatever we need it to be. >> Whatever you need it to be, okay? There's a great joke in physics that the answer is 3. It just depends on what units you pick. I know, physics humor, you can't get enough of it. >> We need to know what theta is. >> We need to know where theta is, right? Theta is going to be rather important. So let's say theta is now right there. If that's theta, what is sine of theta? Well, it's opposite, which is opposite the angle, which in this case would be W over hypotenuse, which in this case is Q. Cosine of theta we said was adjacent over hypotenuse. The adjacent side is right here, so that would be Z divided by the hypotenuse which we said was Q. And then finally tangent of theta is going to be opposite W over adjacent Z. Okay? In physics, we're going to end up working with X and Y's, but those are just variables. We can use any variables we want. All right? Hopefully, that is reasonably clear.