Understanding Ax = x cos(angle) and Ay = y sin(angle) in Physics

[member 529879]

In physics we use the formulas Ax = x cos(angle) and Ay = y sin(angle) to find the x or y component of a vector. How do these formulas work, and what all can they be used for?

 

[SteamKing]

In physics we use the formulas Ax = x cos(angle) and Ay = y sin(angle) to find the x or y component of a vector. How do these formulas work, and what all can they be used for?

Have you studied trigonometry?

 

[member 529879]

I'm taking my first year of high school physics and algebra/trig this year so I don't know too much about trigonometry as of now.

 

[jtbell]

Many physical quantities have both a magnitude and a direction: velocity, acceleration, force, momentum, etc. We call these vector quantities. In everyday language it's most natural to describe them using the magnitude and either one angle (for two-dimensional motion) or two angles (for three-dimensional motion). However, many mathematical operations (like adding two vectors) are easier if you use x- and y- (and possibly z-) components. So you spend a lot of time in intro physics courses learning how to convert between magnitude+angle(s) and components. That's where the trigonometry comes in.

If you need something to supplement your textbook for the mathematical details, try this:

http://hyperphysics.phy-astr.gsu.edu/hbase/vect.html

It does assume that you already know basic trig stuff like the definitions of sine and cosine.

 

[Edvin]

If your question is related to basic trig:
Given a right triangle...

sin(angle) = opposite_length / hypotenuse_length
so, multiplying both side by hypotenuse_length gives us:
opposite_length = hypotenuse * sin(angle)
Thus, Ay = A sin(angle)

Similarly,
cos(angle) = adjacent / hypotenuse_length
so, multiplying both side by hypotenuse_length gives us:
adjacent_length = hypotenuse_length * cos(angle)
Thus, Ax =A cos(angle)

In many physics problems you'll find that the hypotenuse_length is represented by velocity or force.

Here is couple more google links 1, 2, ...