Electronic Components/Coordinate Geometry.

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Coordinate Geometry.
Coordinate Geometry.  
QUESTION: Dear Deirdre

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 only difference is representational. It would be no different than representing the Earth with the South pole at the top or writing left to right vs. right to left or bottom to top on a page.
I presume that this might be a bit unconventional, but it does nothing to the underlying mathematics. To see what it might look like, one could just take an old oscilloscope and rotate the tube 90 degrees.

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

Sine Wave
Sine Wave  
QUESTION: Dear Deirdre

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: The only change in the plot is orientation - you are swapping time and value axes, nothing else. It is like taking the graph paper and rotating it. There is no difference in the mathematics - just the presentation. Instead of a horizontal wave, you'll have one that is oriented on the vertical axis. Other than that, there is no difference.


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

Sine Inverse Curve
Sine Inverse Curve  
QUESTION: Dear Deirdre

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

Answer
It's not a "different" wave - it's the same wave plotted differently - it's just like rotating the graph paper (and taking a mirror image). The data is the same, the mathematics is the same. The only difference is presentation. The mathematical function is not dependent on the type of graph plotted by the data.
We can also plot data on paper using polar rather than rectangular coordinates - this doesn't change the function or the data.
What might help you is this animated .gif of a sin function converted from the standard X-Y graph, then swapping the X and Y axes, and then converting it to polar coordinates. These are all equal graphs of the same function. The only difference is presentation, but they are all a sine wave.

http://en.wikipedia.org/wiki/File:Cartesian_to_polar.gif

The graph illustrates that changing the orientation does not change a sine wave into an inverse sine wave - it is merely presenting a sine wave differently.

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Deirdre Hebert

Expertise

I can answer most questions regarding electronic components, what they are and how to use them.

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I worked for a number of years in the electronic component testing industry, designing and building automated test equipment for the electronic manufacturing industry.

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Numerous technical manuals for the equipment we built.

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UNH, CCAF and others

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General Electric, Motorola, Ford, Sensonor and others.

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