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What are the coordinates of point A?
The coordinates of point A are (2, 4).
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Which coordinates?
The coordinates refer to a set of values that pinpoint a specific location on a map or graph. These values typically include a pair of numbers, such as latitude and longitude, that help identify the exact position of a point on the Earth's surface. Coordinates are essential for navigation, mapping, and locating specific places accurately.
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How to calculate the polar coordinates of point A, given in Cartesian coordinates as A(1,6)?
To calculate the polar coordinates of point A(1,6) given in Cartesian coordinates, we can use the formulas r = sqrt(x^2 + y^2) and θ = arctan(y/x). First, calculate the value of r by substituting the x and y coordinates of point A into the formula r = sqrt(1^2 + 6^2) = sqrt(1 + 36) = sqrt(37). Next, calculate the value of θ by substituting the x and y coordinates of point A into the formula θ = arctan(6/1) = arctan(6) ≈ 1.405 radians or 80.54 degrees. Therefore, the polar coordinates of point A(1,6) are (sqrt(37), 1.405 radians) or (sqrt(37), 80.54 degrees).
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How do you calculate the polar coordinates of point A, given in Cartesian coordinates as A(1,6)?
To calculate the polar coordinates of point A(1,6) given in Cartesian coordinates, we can use the formulas r = sqrt(x^2 + y^2) and θ = arctan(y/x). First, calculate the value of r by substituting the x and y coordinates of point A into the formula: r = sqrt(1^2 + 6^2) = sqrt(1 + 36) = sqrt(37). Next, calculate the value of θ by substituting the x and y coordinates of point A into the formula: θ = arctan(6/1) = arctan(6) ≈ 1.405 radians. Therefore, the polar coordinates of point A(1,6) are (sqrt(37), 1.405 radians).
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How can Cartesian coordinates be converted to polar coordinates?
To convert Cartesian coordinates (x, y) to polar coordinates (r, θ), we can use the following formulas: r = √(x^2 + y^2) - to find the distance from the origin to the point. θ = arctan(y/x) - to find the angle θ that the line connecting the point to the origin makes with the positive x-axis. These formulas allow us to represent a point in the Cartesian plane in terms of its distance from the origin and the angle it makes with the positive x-axis.
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What is the difference between Cartesian coordinates and polar coordinates?
Cartesian coordinates are a system that uses two perpendicular axes (x and y) to locate a point in a plane by its distance from each axis. Polar coordinates, on the other hand, use a distance from the origin (r) and an angle (θ) to locate a point in a plane. In Cartesian coordinates, distances are measured horizontally and vertically, while in polar coordinates, distances are measured radially and angularly. The conversion between the two systems involves trigonometric functions.
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What are the differences between polar coordinates and Cartesian coordinates?
Polar coordinates use a distance and an angle to locate a point, while Cartesian coordinates use x and y coordinates. In polar coordinates, the distance is represented by the radius and the angle is measured counterclockwise from the positive x-axis. In Cartesian coordinates, the x-axis and y-axis are perpendicular to each other, forming a grid system. Polar coordinates are often used to describe circular or radial patterns, while Cartesian coordinates are more commonly used in everyday applications.
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What is the difference between polar coordinates and Cartesian coordinates?
Polar coordinates represent a point in a plane by its distance from a fixed point (the pole) and the angle it makes with a fixed axis (the polar axis). In contrast, Cartesian coordinates represent a point by its distance from two perpendicular axes (x and y axes). While polar coordinates are more suitable for representing circular and radial patterns, Cartesian coordinates are better for representing linear relationships and precise measurements in a plane.
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