Calculating Arc Length on a Circle with Cartesian Coordinates

[Kikki:)]

Homework Statement

The Carteian coordinates of a point on a circle with its center at the origin are [0.40, 0.30]. What is the arc length measured counterclockwise on the circle from the positive x-axis to this point?

Homework Equations

The Attempt at a Solution

Wouldn't they be the complete opposite as in negative cordinates. Since going counter clockwise is - and clock wise is + . I ues the main question I'm asking is what does it mean with the coordinates, does it mean that 0.4 left and 0.3 up? But then what would the radius be? I guess I need a little help getting started otherwise I can do the rest I think on my own. :] You all have helped me so much! I'm not great at torque and rotational motion. More better at the concepts, I'm hrrible at algebra.

 

[QuarkCharmer]

It says that the center is at the origin, point (0,0), and a point on the circle is (.40,.30). Isn't there some way that you could find the radius from that? Once you have that, is there some sort of "relationship" between the radius of a circle and it's diameter?

Wouldn't they be the complete opposite as in negative cordinates. Since going counter clockwise is - and clock wise is + .

You are still measuring a distance (of the arc), are you not?

 

[Kikki:)]

It says that the center is at the origin, point (0,0), and a point on the circle is (.40,.30). Isn't there some way that you could find the radius from that? Once you have that, is there some sort of "relationship" between the radius of a circle and it's diameter?

So if its positioned at (0,0) then that would mean that the radius is 4 and the 8. Yes there is because radius is half of the diameter.

So this is basically an easy question but I'm just making it hard.

 

[QuarkCharmer]

I meant circumference, not diameter! Sorry about that.

Isn't there some relationship between the radius and the circumference? (think about what a radian is)

The radius is going to be the value given by the distance formula between the given points right?

 

[Kikki:)]

I meant circumference, not diameter! Sorry about that.

Isn't there some relationship between the radius and the circumference? (think about what a radian is)

The radius is going to be the value given by the distance formula between the given points right?

Yes because 2$$\pi$$r and that is also to find the radian. You take the radius and use that to go around the make up of the circle which is usualy 6.28 with just a circle. So the formula for radian = arc length/radius .

 

[QuarkCharmer]

Using the formula, arc-length = theta*radius, can't you figure out the arc length?