# Electronic Components/Coordinate Geometry.

Question

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.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) ?

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
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 ?

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
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 ?

Thanks & Regards,
Prashant S Akerkar

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.
Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Dear Deirdre Thank you. Thanks & Regards, Prashant S Akerkar

Electronic Components

Volunteer

#### Deirdre Hebert

##### Expertise

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

##### Experience

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

Publications
Numerous technical manuals for the equipment we built.

Education/Credentials
UNH, CCAF and others

Past/Present Clients
General Electric, Motorola, Ford, Sensonor and others.