In conclusion, the coordinate system is a powerful tool that allows us to precisely locate and describe points in space. It has numerous applications and is fundamental in many areas of study. Understanding how to interpret and work with coordinates opens up a whole new world of possibilities.
A coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space. The Cartesian coordinate system is the prototypical example of a coordinate system. In the plane, two perpendicular lines are chosen and the coordinates of a point are taken to be the signed distances to the lines. In three dimensions, three mutually orthogonal planes are chosen and the three coordinates of a point are the signed distances to each of the planes. The polar coordinate system is another common coordinate system for the plane. A point is chosen as the pole and a ray from this point is taken as the polar axis. For a given angle θ, there is a single line through the pole whose angle with the polar axis is θ (measured counterclockwise from the axis to the line). Then there is a unique point on this line whose signed distance from the origin is r for given number r. For a given pair of coordinates (r, θ) there is a single point, but any point is represented by many pairs of coordinates. For example, (r, θ), (r, θ + 2π) and (−r, θ + π) are all polar coordinates for the same point. The pole is represented by (0, θ) for any value of θ.
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In conclusion, the coordinate system is a powerful tool that allows us to precisely locate and describe points in space. It has numerous applications and is fundamental in many areas of study. Understanding how to interpret and work with coordinates opens up a whole new world of possibilities.
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Answer:
A coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space. The Cartesian coordinate system is the prototypical example of a coordinate system. In the plane, two perpendicular lines are chosen and the coordinates of a point are taken to be the signed distances to the lines. In three dimensions, three mutually orthogonal planes are chosen and the three coordinates of a point are the signed distances to each of the planes. The polar coordinate system is another common coordinate system for the plane. A point is chosen as the pole and a ray from this point is taken as the polar axis. For a given angle θ, there is a single line through the pole whose angle with the polar axis is θ (measured counterclockwise from the axis to the line). Then there is a unique point on this line whose signed distance from the origin is r for given number r. For a given pair of coordinates (r, θ) there is a single point, but any point is represented by many pairs of coordinates. For example, (r, θ), (r, θ + 2π) and (−r, θ + π) are all polar coordinates for the same point. The pole is represented by (0, θ) for any value of θ.
Step-by-step explanation: I hope this helps! kindly drop thanks and mark as brainliest :)