Understanding Rotating Coordinate Systems: A Visual Approach

[xzibition8612]

Homework Statement

http://www.brookscole.com/math_d/sp...athematica_labs/14-multipleintegrals/p05a.pdf

Homework Equations

The Attempt at a Solution

My question concerns the (1) and (2) next to the figure of the rotating coordinate system.

x=ucos(theta)-vsin(theta)
y=ucos(theta)...
...

So my problem is I can't visualize it. I can visualize that u = ucos(theta) + usin(theta), but I don't get how u = xcos(theta) + ysin(theta).
If anyone can explain or try to visually show it to me would be great. Thanks.

 

[utku]

Hi,xzibition8612.

Multiply both side of equatlity (1) x=ucos(theta)-vsin(theta) with cos(theta) and both of equality y=ucos(theta)...with sin(theta) you will see some terms will vanish.And you will get your answer...

 

[xzibition8612]

ok i did as you said and got u = sin(theta)y + xcos(theta) which is (2). I still don't get how come u is this quantity. I mean in a visual manner. I'm not so smart to understand it abstractly. Sorry for my poor intelligence.