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QUESTION: Dear Prof Randy

http://en.wikipedia.org/wiki/Analytic_geometry

http://www.mathopenref.com/coordintro.html

http://www.math.com/school/subject3/lessons/S3U1L2GL.html

http://c-schools.net/PPT/Coordinate%20Geometry.ppt

http://www.youtube.com/watch?v=7h74ad7IWiI

http://www.math.wisc.edu/~robbin/461dir/coordinateGeometry.pdf

http://www.wolframalpha.com/examples/CoordinateGeometry.html

What could be the Impact to different disciplines and applications

of mathematics if Point (x,y) is replaced with Point (y,x).

i.e. x coordinate = Horizontal axis

y coordinate = Vertical axis

Now instead of this standard convention, implement the following

given below

i.e. x coordinate = Vertical axis

y coordinate = Horizontal axis

For examples :

1st Quadrant Point A(3,2) will become Point A(2,3)

2nd Quadrant Point B(-2,3) will become Point B(3,-2)

3rd Quadrant Point C(-3,-4) will become Point C(-4,-3)

4th Quadrant Point D(2,-3) will become Point D(-3,2)

i.e. because the Points are now represented as y,x instead of x,y,

the Plotting of Points A,B,C,D on graph paper will be now different.

Can there be any impact while plotting Graphs viz Sine,Cosine, Tangent waves etc, vector algebra and other applications of mathematics similar to Coordinate Geometry if Point F (x,y) is represented as Point F(y,x) ?

Awaiting your reply,

Thanks & Regards,

Prashant S Akerkar

ANSWER: The impact of switching (x,y) to (y,x) can be viewed in a couple of ways.

First, it doesn't really matter what letters you assign to the axes as long as you are consistent.

Second, flipping the coordinates can be seen as just flipping a point in the plane about the line y = x, that is, creating a mirror image of the point. You can see this easily by plotting the points you listed in your question. This transformation is also given by the simple matrix manipulation

( 0 1 ) ( x ) ( y )

( 1 0 ) ( y ) = ( x ).

Third, switching axes will flip a curve in the x-y plane. For example, an ellipse will have the major and minor axes interchanged. Less symmetric curves will also be flipped across the y = x line.

Fourth, you can, in a sense, "flip" the functional relation y = f(x) to be x = f^(-1)(y), which is to take the inverse. However, I don't think this is what you have in mind.

In short, flipping the coordinates doesn't necessarily do much of anything. Any consequences can be accomodated by applying standard mathematical techniques.

Randy

---------- FOLLOW-UP ----------

QUESTION: Dear Prof Randy

Thank you.

http://en.wikipedia.org/wiki/Sine_wave

Can the interchange of x - horizontal axes to y - horizontal axis and y - vertical axis to x - horizontal axes will effect the Sine, Cosine, Tangent and other trigonometric curves plotting ?

i.e. Will the Sine Wave plotted now will be seen in a different wave ?

This could be because the coordinates (0, 30 degree, 45 degree, 60 degree, 90 degree, 120 degree, 150 degree, 180 degree or respective conversion to radiant etc) will be plotted now on the Y axis ?

Awaiting your reply,

Thanks & Regards,

Prashant S Akerkar

ANSWER: Instead of propagating horizontally, the sine wave will propagate vertically. So, take your image and rotate it 90 degrees and you'll see what it looks like with sin(y) = x.

---------- FOLLOW-UP ----------

QUESTION: Dear Prof Randy

Thank you.

http://www.intmath.com/analytic-trigonometry/7-inverse-trigo-functions.php

Can the interchange of x - horizontal axes to y - horizontal axis and y - vertical axis to x - horizontal axes will effect the Sine Inverse, Cosine Inverse, Tangent Inverse and other trigonometric curves plotting ?

i.e. Will the Sine Inverse Wave plotted now will be seen in a different wave ?

Awaiting your reply,

Thanks & Regards,

Prashant S Akerkar

Your picture really tells it all. If you switch x and y, the curve reflects about the y = x line. This is actually a very good representation of the "effect".

You should think about what the curves represent. The sine of a number can be interpreted as a ratio, as in trigonometry. The arcsin (sine inverse) of a number x (which, by the way, has to be -1<x<1) can be interpreted an an angle. Two different animals. So calling arcsin a "wave" is not really accurate.

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Comment | Dear Prof Randy Thank you. Thanks & Regards, Prashant S Akerkar |

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