# Compact disc question

• March 21st 2010, 03:28 PM
florx
Compact disc question
A compact disc is 120 millimeters across with a center hole of diameter 15 millimeters. The center of the disc is at the origin. What are the coordinates of the points at which the inner and outer edge intersect the positive x-axis? What are the coordinates of the points at which the inner and outer edges cut a line making an angle θ with the positive x-axis?

So for number one, it says "What are the coordinates of the points at which the inner and outer edge intersect the positive x-axis"
For the inner circle wouldn't we take it's radius which is 7.5 and so the points for the inner edge that intersect the positive x-axis be (7.5,0)?

As for the outer edge wouldn't we take 120 - 15 so it would be 105. Take the radius of that and it would be 52.2. So the point that the outer edge touches the positive x-axis would be 52.2?

Please confirm if I did the first part of the problem correctly.

As for the second part of the question, wouldn't we need to create some sort of formula like sin θ or something? I don't quite understand how to do part 2.

• March 21st 2010, 03:54 PM
skeeter
Quote:

Originally Posted by florx
A compact disc is 120 millimeters across with a center hole of diameter 15 millimeters. The center of the disc is at the origin. What are the coordinates of the points at which the inner and outer edge intersect the positive x-axis? What are the coordinates of the points at which the inner and outer edges cut a line making an angle θ with the positive x-axis?

So for number one, it says "What are the coordinates of the points at which the inner and outer edge intersect the positive x-axis"
For the inner circle wouldn't we take it's radius which is 7.5 and so the points for the inner edge that intersect the positive x-axis be (7.5,0)?

As for the outer edge wouldn't we take 120 - 15 so it would be 105. Take the radius of that and it would be 52.2. So the point that the outer edge touches the positive x-axis would be 52.2?

Please confirm if I did the first part of the problem correctly.

As for the second part of the question, wouldn't we need to create some sort of formula like sin θ or something? I don't quite understand how to do part 2.

inner ... $(7.5,0)$
outer ... $(60,0)$
inner ... $(7.5\cos{\theta},7.5\sin{\theta})$
outer ... $(60\cos{\theta},60\sin{\theta})$