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SOLUTION:
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In this question, we are given the following:
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The details of the solution are as follows:
The cartesian coordinate system, also known as a rectangular coordinate system is done on two coordinate axes which we call as x-axis and y-axis and which are perpendicular to each other .
The distance-time curve or the velocity -time curve can be plotted on the rectangular coordinate axis with distance on the y-axis and the time on the x-axis .The slope of the s-t curve gives velocity and v-t curve will give acceleration .In rectangular coordinate system the points are of the form (x,y) .
Polar coordinate system - let us take an example to understand this .We consider an equation of a circle with centre at the origin (0,0) .We know that equation of a circle is given by :
x2+y2=r2 ,In the rectangular coordinate system the points on the circle will be of the form (x,y) but in case of polar coordinates the point on the circle will be denoted by (rcosθ,rsinθ) where 'r' is the radius of the circle .We can change the equation of a circle given in rectangular coordinates to the polar coordinates by making the substitution x=rcosθ and y=rsinθ and we will get the desired equation in polar cordinates .
In case of complex coordinate system , as we know that a complex number consists of a real part and an imaginary part where the real part is plotted on the x-axis and the imaginary part is plotted on the y-axis .The absolute value of a complex number is its distance from the origin .
The distance between two points is given by √ (x2 − x1)2 + (y2 − y1)2 .In this manner the distance between two complex numbers can also be calculated .The common thing between the three coordinate system is that all of them are plotted on coordinate axis which are perpendicular to each other and unique thing is that rectangular coordinate system involves plotting of numbers whereas in case of polar coordinate system there is a reference angle involved as the coordinates are of the form (rcosθ,rsinθ) .In case of complex coordinate system ,it looks like cartesian coordinate system as imaginary part is plotted on the vertical axis and the real part is plotted on the horizontal axis .
Plotting on different coordinate axis makes the calculation relatively easier and it becomes easier to visualise the given problem that are some of the advantages . Coordinate system have their use to represent the location of imagery and observations and enable global positioning system .
Some of the disadvantages of coordinate system are that they may introduce errors in the desired result and there may be loss of accuracy and exactness .There may be approximations in the size ,location and shapes and this may cause relative errors and less precision .Thus there are limitations .
