What are the mathematical concepts used to describe angles in three dimensions?

[Nano-Passion]

We usually describe angles in two dimensions (x and y plane). What is the mathematics behind three dimensions?

 

[Jocko Homo]

We usually describe angles in two dimensions (x and y plane). What is the mathematics behind three dimensions?

I don't get it. You're an undergrad in physics and you're asking this question? Why don't you already know?

It's really no different. When you talk about the angle between things in three dimensions, you can think of them as being on some plane oriented in those three dimensions and then think about the angle in relation to that plane, just as you would with the familiar x-y plane...

 

[Char. Limit]

Actually, I'd say we usually describe angles in two-dimensions with theta and r. That is, an angle from the designated "zero line", and a distance from the origin. In three dimensions, we simply add another angle, usually phi, that I call the "vertical angle", or the angle between the line and the x-y plane.

 

[Nano-Passion]

I don't get it. You're an undergrad in physics and you're asking this question? Why don't you already know?

It's really no different. When you talk about the angle between things in three dimensions, you can think of them as being on some plane oriented in those three dimensions and then think about the angle in relation to that plane, just as you would with the familiar x-y plane...

I'm in Calculus based Classical Mechanics at the moment. We haven't gone into figuring out angles in three-dimensions.

Actually, I'd say we usually describe angles in two-dimensions with theta and r. That is, an angle from the designated "zero line", and a distance from the origin. In three dimensions, we simply add another angle, usually phi, that I call the "vertical angle", or the angle between the line and the x-y plane.

I'm surprised its that simple. I've read around and seen that sometimes the math isn't incredibly accurate (such as near pi with using cos).

As you see, there is a very distinct loss of accuracy in 'acos' for angles
near pi. Some seven entire decimal places have been lost - that is,
errors are several million times as large as normal. On the other hand,
the angle near pi/2 yields the customary 1 in 2^52 accuracy.

 

[CellCoree]

In three dimensions, angles are described using three coordinates (x, y, and z) instead of just two. This allows for a more accurate representation of the angle in space. The mathematics behind three dimensions involves using trigonometric functions such as sine, cosine, and tangent to calculate the angle between two vectors or lines in three-dimensional space. Additionally, the Pythagorean theorem is used to find the length of the hypotenuse in a right triangle in three dimensions. Other mathematical concepts such as vectors, dot products, and cross products are also used to calculate angles in three dimensions. Overall, the mathematics behind three dimensions allows us to accurately measure and describe angles in a three-dimensional space, which is crucial in many fields such as engineering, physics, and computer graphics.