Polar Coordinates: Traveling Clockwise from (0,-1) to (0,1)

In summary, polar coordinates are a system of locating points on a plane using a distance from the origin and an angle from a reference axis. To travel clockwise from (0,-1) to (0,1) in polar coordinates, one would start at the point (0,-1) and move in a circular motion around the origin until reaching the point (0,1). The reference axis in polar coordinates is a fixed line passing through the origin, and the distance from the origin is known as the radius. Additionally, polar coordinates can be extended to three dimensions by adding a third coordinate, known as the z-coordinate. This allows for the location of points in a three-dimensional space using a distance, angle, and height from the origin.
  • #1
phamdat1202
4
0

Homework Statement


the circle travels clockwise from (0,-1) to (0,1)
write down the parameterization in term of t

Homework Equations


The Attempt at a Solution


x=cost(t)
y=-sin(t)

i'm not sure about the sign of the polar coordinate, how to find the sign?
 
Last edited:
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  • #2
Think about the extremes, what should the values be at t = 0? what about t = pi?
 

1. What are polar coordinates?

Polar coordinates are a system of locating points on a plane using a distance from the origin and an angle from a reference axis.

2. How do you travel clockwise from (0,-1) to (0,1) in polar coordinates?

To travel clockwise from (0,-1) to (0,1) in polar coordinates, you would start at the point (0,-1) and move in a circular motion around the origin until you reach the point (0,1). This would involve increasing the angle while keeping the distance from the origin constant.

3. What is the reference axis in polar coordinates?

The reference axis in polar coordinates is a fixed line passing through the origin and used as a starting point for measuring angles.

4. What is the distance from the origin in polar coordinates?

The distance from the origin in polar coordinates is known as the radius and is measured in units such as meters or feet.

5. Can you use polar coordinates to locate points in three-dimensional space?

Yes, polar coordinates can be extended to three dimensions by adding a third coordinate, known as the z-coordinate. This allows for the location of points in a three-dimensional space using a distance, angle, and height from the origin.

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