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coordinates. polar coordinate system, gives the co-ordinates of a point with reference to a point O and a half line or ray starting at the point O. We will look at polar coordinates for points in the xy-plane, using the origin (0; 0) and the positive x-axis for reference.
We need two measurements, 𝑟𝑟 and 𝜃𝜃, to describe a point, 𝑃𝑃, in polar coordinates. • 𝑟𝑟 is the distance of the point 𝑃𝑃 from the pole (the origin 𝑂𝑂). • 𝜃𝜃 is the angle measured anticlockwise between the initial line
The first number u is taken to be a distance and the second number v is taken to be an angle (usually in radians). To be explicit about this, we will denote the pair as (r, θ) instead of (u, v). The numbers r and θ can be positive, negative or zero. Here are the rules for the polar coordinate system: 1.
The distance is given by a positive number r. Those are the polar coordinates of the point, where x and y are the rectangular coordinates. The angle 6 is measured from the horizontal. Suppose the distance is 2 and the direction is 30"or 4 6 (degrees preferred by flight controllers, radians by mathemati- cians).
However, the same point P can be located by using polar coordinates r,θ where r is the distance of P from the origin and θ is the angle, measured anti-clockwise, that the line OP makes when measured from the positive x-direction.
8.1 Polar Coordinates. MIT OpenCourseWare is a web based publication of virtually all MIT course content. OCW is open and available to the world and is a permanent MIT activity.
Any point P can be described by the coordinates ( , ), where is the radial distance from the point to the origin (also referred to as the pole) and is the angle subtended by the radial line connecting the point to the origin and the x-axis. Note that the axis is often called the initial line. = sin2 .
