What are polar coordinates?
polar coordinates are an expressive position on a two -dimensional plane. Cartesian coordinates, also called rectangular coordinates, use the distance in each of the two dimensions to find a point, but the polar coordinates use the angle and distance. The distance is sometimes referred to as a radius.
rectangular coordinates are usually marked (x, y) , where x and y are distances along these relevant axes. In a similar way, polar coordinates are expressed as (r, θ) . A letter r is a distance from origin at an angle represented by the Greek letter Theta, θ , where r may be a positive or negative number. If a negative distance is used, the size of the distance does not change, but the direction is performed opposite the angle θ on the other side of origin. The point in the polar coordinate system can be described as a representative vector, with the size of r , the direction θ and a direction of direction, which is a sign r .
Translation between rectangular and polar coordinates can be achieved by means of trigonometric formulas. The following formulas can be used to convert from rectangular to polar: θ = tan (y/x) and r = ( x 2
polar coordinates tend to be used for any situation in which rectangular coordinates would prove difficult or unpleasant to use and vice versa. Any application involving circular geometry or radial movement is ideal for polar coordinates because these geometry can be described relative poisonNodeché equations in the polar coordinate system; Their graphs have a more curved or circular look compared to graphs on rectangular coordinate systems. As a result, polar coordinates have the use of representing phenomena models in the real world that have similarly rounded shapes.
The application of polar coordinates are quite diverse. The graphs of the polar coordinates were used to model the sound fields produced by different locations of the speakers or areas where different types of microphones can best pick up the sound. The polar coordinates have very important modeling of orbital movements in astronomy and space travel. They are also a graphical basis for the famous Euler formula, which is regularly applied in mathematics for representation and manipulation of complex numbers.
as well as their rectangular counterparts, polar coordinates need not be limited to only two dimensions. If you want to express values in three dimensions, the second angle represented by the Greek letter Phi, &pawal; , can be added to the coordinate system. Thus, any point can be placed from the origin of a fixed distance and two angles and can be assigned to the (R, θ, φ) coordinates. When this type of nomenclature is used to monitor and search for points in three -dimensional space, the coordinate system is marked as a spherical coordinate system. This type of geometry is sometimes referred to as the use of polar spherical coordinates.
spherical coordinates are in fact a known application-they are used to map the ground. The angle θ is usually a geographic width and is limited to minus-90 degrees and 90 degrees, while the angle φ is length and is held to minus-180 and 180 degrees. In this application, r can sometimes be ignored, but more often used for an expression of altitude above the average sea level.