# Thread: coordinates of a paint spot

1. ## coordinates of a paint spot

A wheel whose radius is 1 is placed so that its center is at (3,2).
A paint spot on the rim is found at (4,2). The wheel is spun theta degrees in the counterclockwise direction. Now what are the coordinates of that paint spot?

I tried using matrix cos -sin ( 4)
sin cos (2)

it doesn't seem to work.

2. Originally Posted by Veronica1999
A wheel whose radius is 1 is placed so that its center is at (3,2).
A paint spot on the rim is found at (4,2). The wheel is spun theta degrees in the counterclockwise direction. Now what are the coordinates of that paint spot?

I tried using matrix cos -sin ( 4)
sin cos (2)

it doesn't seem to work.

hey veronica..
if you draw a figure which has the original position of the paint spot and the rotated position of the spot ... and if you label the figure and attach it here then i can explain to you what is wrong. also re-post your attempt with that.

3. Originally Posted by Veronica1999
A wheel whose radius is 1 is placed so that its center is at (3,2).
A paint spot on the rim is found at (4,2). The wheel is spun theta degrees in the counterclockwise direction. Now what are the coordinates of that paint spot?
This is no more than asking about the parametric for of the equation of a circle,
Let's say that the circle has center (h,k) and radius r.
The parametric equation of that circle is:
$\left\{ {\begin{array}{*{20}c} {x(\theta ) = r\cos (\theta ) + h} \\ {y(\theta ) = r\sin (\theta ) + k} \\ \end{array} ,\,0 \leqslant \theta \leqslant 2\pi } \right.$

4. Thanks, I see the problem was very simple.
Pls find attached work. I wonder why i couldn't use matrices.
Does the center have to be at the origin>

5. Originally Posted by Veronica1999
Thanks, I see the problem was very simple.
Pls find attached work. I wonder why i couldn't use matrices.
Does the center have to be at the origin>
you are right. that working would be right if the centre were at origin. you can construct a matrix which works for this case too but that would look quite different.