Trigonometry: Name Polar Coordinates
This is a free lesson from our course in Trigonometry
 
   
This lesson introduces the basic concepts of the polar coordinate with the help of some examples, practice questions with solution and watching video. It explains how to determine the coordinates of a point in the polar coordinate system. The equation of a curve expressed in polar coordinates is known as a polar equation, and a plot of a curve in polar coordinates is known as a polar plot. Polar coordinate of a point: In the plane we choose a fixed point 'O', and call it the pole.
Additionally we choose an axis x through the pole and call it the polar axis. The pole and the polar axis constitute the basis of the polar coordinate system. (More text below video...)
<h2>Trigonometry - Name Polar Coordinates</h2> <p>polar coordinates, basics, video, polar, equation, triangle, curve, axis, trigonometry help, example, coordinates, solution, ordered pair, point, ray, sine, cosine, polar equation, polar plot, rectangular coordinates, polar coordinate system, right triangle, practice questions, quizzes</p> <p>Polar coordinate of a point: In the plane we choose a fixed point O, and call it the pole. Additionally we choose an axis x through the pole and call it the polar axis. The pole and the polar axis constitute the basis of the polar coordinate system. The polar axis is usually drawn in the direction of the positive x-axis. The pole has been placed at the origin O of a rectangular coordinate system so that the polar axis coincides with the positive x-axis.</p>
Other useful lessons:
Polar -Rectangular Coordinates Conversion
Convert Equation from Polar to Rectangular Form

(Continued from above) The polar axis is usually drawn in the direction of the positive x-axis. The pole has been placed at the origin 'O' of a rectangular coordinate system so that the polar axis coincides with the positive x-axis. Point P has rectangular coordinates (x, y). Point P can also be located by giving the directed angle from the positive x-axis to ray OP at the distance r from the pole to point P. The ordered pair (r, ) gives the polar coordinates of point.

For example: A point with rectangular coordinates (x, y) has coordinates (r, ) in polar coordinate system, where r is the distance from the origin and  is the angle measured counter-clockwise from the x-axis to ray drawn from the origin containing the point (x, y). As this will be a right triangle case, we know that
     r = (x2 + y2),
     = tan-1 (y/x),
     x = r cos
     y = r sin .
The point (r, ) is equivalent to (-r + ) as (r, ) can also be named by using the angle formed by the opposite ray and using -r instead of r.

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