GDB Topic:
Discuss the applications of Polar coordinate System in our daily life with at least 3 examples.
Opening Date: Wednesday, 7th August, 2014 at 12:01 AM
Closing Date: Thursday, 8th August, 2014 at 11:59 PM
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MTH301 GDB no 1 solution:
GPS is a form of polar coordinate system, with 2 angles, North and East, and the radius isn't really necessary. This is obviously used by sat-navs, planes, maps on your phone etc.
Electrical engineers use polar coordinates when designing AC components for your house. You learn at school V= I R but actually, it's a vector equation. The result impedance, influences how much voltage you get depending on the voltage. So electrical engineers use polar notation of vectors to make sure all your household products produce the power they're supposed to.
Clocks. Analogue Clocks work on the principle of defining time by 2 angles and 2 lengths: the position of the point of each hand.
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Solar Energy system are designed according to Polar coordinates polarities...
Polar coordinates are two-dimensional and thus they can be used only where point positions lie on a single two-dimensional plane. They are most appropriate in any context where the phenomenon being considered is inherently tied to direction and length from a center point. For instance, the examples above show how elementary polar equations suffice to define curves—such as the Archimedean spiral—whose equation in the Cartesian coordinate system would be much more intricate. Moreover, many physical systems—such as those concerned with bodies moving around a central point or with phenomena originating from a central point—are simpler and more intuitive to model using polar coordinates. The initial motivation for the introduction of the polar system was the study of circular and orbital motion.
Position and navigation
Polar coordinates are used often in navigation, as the destination or direction of travel can be given as an angle and distance from the object being considered. For instance, aircraft use a slightly modified version of the polar coordinates for navigation. In this system, the one generally used for any sort of navigation, the 0° ray is generally called heading 360, and the angles continue in a clockwise direction, rather than counterclockwise, as in the mathematical system. Heading 360 corresponds to magnetic north, while headings 90, 180, and 270 correspond to magnetic east, south, and west, respectively.[21] Thus, an aircraft traveling 5 nautical miles due east will be traveling 5 units at heading 90 (read zero-niner-zero by air traffic control).[22]
Modeling
Systems displaying radial symmetry provide natural settings for the polar coordinate system, with the central point acting as the pole. A prime example of this usage is the groundwater flow equation when applied to radially symmetric wells. Systems with a radial force are also good candidates for the use of the polar coordinate system. These systems include gravitational fields, which obey the inverse-square law, as well as systems with point sources, such as radio antennas.
Radially asymmetric systems may also be modeled with polar coordinates. For example, a microphone's pickup pattern illustrates its proportional response to an incoming sound from a given direction, and these patterns can be represented as polar curves. The curve for a standard cardioid microphone, the most common unidirectional microphone, can be represented as r = 0.5 + 0.5sin(θ) at its target design frequency.[23] The pattern shifts toward omnidirectionality at lower frequencies
GPS is a form of polar coordinate system, with 2 angles, North and East, and the radius isn't really necessary. This is obviously used by sat-navs, planes, maps on your phone etc.
Electrical engineers use polar coordinates when designing AC components for your house. You learn at school V= I R but actually, it's a vector equation. The result impedance, influences how much voltage you get depending on the voltage. So electrical engineers use polar notation of vectors to make sure all your household products produce the power they're supposed to.
Clocks. Analogue Clocks work on the principle of defining time by 2 angles and 2 lengths: the position of the point of each hand.
Polar Coordinates
For certain functions, rectangular coordinates (those using x-axis and y-axis) are very inconvenient. In rectangular coordinates, we describe points as being a certain distance along the x-axis and a certain distance along the y-axis.
polar coordinates
But certain functions are very complicated if we use the rectangular coordinate system. Such functions may be much simpler in the polar coordinate system, which allows us to describe and graph certain functions in a very convenient way.
Polar coordinates work in much the same way that we have seen in trignometry(radians and arc length, where we used r and θ) and in the polar form of complex numbers (where we also saw r and θ).
In polar coordinates, we describe points as being a certain distance ® from the pole (the origin) and at a certain angle (θ) from the positive horizontal axis (called the polar axis).
COORDINATES AND AXES.
Though it is named after the French mathematician and philosopher René Descartes (1596-1650), who first described its principles, the Cartesian system owes at least as much to Pierre de Fermat (1601-1665). Fermat, a brilliant French amateur mathematician—amateur in the sense that he was not trained inmathematics, nor did he earn a living from that discipline—greatly developed the Cartesian system.
A coordinate is a number or set of numbers used to specify the location of a point on a line, on a surface such as a plane, or in space. In the Cartesian system, the x-axis is the horizontal line of reference, and the y-axis the vertical line of reference. Hence, the coordinate (0, 0) designates the point where the x-and y-axes meet. All numbers to the right of 0 on the x-axis, and above 0 on the y-axis, have a positive value, while those to the left of 0 on the x-axis, or below 0 on the y-axis have a negative value.
GPS is a form of polar coordinate system, with 2 angles, North and East, and the radius isn't really necessary. This is obviously used by sat-navs, planes, maps on your phone etc.
Electrical engineers use polar coordinates when designing AC components for your house. You learn at school V= I R but actually, it's a vector equation. The result impedance, influences how much voltage you get depending on the voltage. So electrical engineers use polar notation of vectors to make sure all your household products produce the power they're supposed to.
Clocks. Analogue Clocks work on the principle of defining time by 2 angles and 2 lengths: the position of the point of each hand.
Hope this helps!
MTH-301 GDB IDEA SOLUTION
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