Polar and Rectangular conversion
07-26-2018, 07:01 PM (This post was last modified: 07-27-2018 11:28 AM by DrD.)
Post: #1
 DrD Senior Member Posts: 1,133 Joined: Feb 2014
Polar and Rectangular conversion
rectangular_coordinates(-(sqrt(2)),(π/4)) ==> [-1,-1]

polar_coordinates(-1,-1) ==> [sqrt(2),(3/4)*π]
polar_coordinates([-1,-1]) ==> [sqrt(2),(-3/4)*π]

polar_coordinates() expects a point, and returns a vector.
rectangular_coordinates() expects a vector and returns a vector.

This is confusing for infrequent users of these commands. The polar_coordinates() command can lead to an incorrect result, if a vector is supplied as the argument, such as might be the case if the result of rectangular_coordinates() was being re-used there.

NOTE: I was using the emulator, and I have been noticing some odd behaviors (including the above). After performing a reset, I am now getting the same result from polar_coordinates() whether or not a point or vector is used. I apologize for this diversion!

-Dale-
07-27-2018, 04:47 AM
Post: #2
 Stevetuc Senior Member Posts: 303 Joined: Jan 2014
RE: Polar and Rectangular conversion
(07-26-2018 07:01 PM)DrD Wrote:  rectangular_coordinates(-(sqrt(2)),(π/4)) ==> [-1,-1]

polar_coordinates(-1,-1) ==> [sqrt(2),(3/4)*π]
polar_coordinates([-1,-1]) ==> [sqrt(2),(-3/4)*π]

polar_coordinates() expects a point, and returns a vector.
rectangular_coordinates() expects a vector and returns a vector.

This is confusing for infrequent users of these commands. The polar_coordinates() command can lead to an incorrect result, if a vector is supplied as the argument, such as might be the case if the result of rectangular_coordinates() was being re-used there.

polar_coordinates([-1,-1]) ==> [sqrt(2),(-3/4)*π] is correct.
The original polar coordinate -(sqrt(2)),(π/4) has a rotation of π added due to the negative sign of the magnitude.
The angle sum (π+π/4) can be written +5/4*π or -3/4*π which is the result given by polar_coordinates([-1,-1])
Using polar_coordinates without the vector is omitting the sign of the angle.
07-27-2018, 10:54 AM
Post: #3
 ijabbott Senior Member Posts: 1,211 Joined: Jul 2015
RE: Polar and Rectangular conversion
(07-26-2018 07:01 PM)DrD Wrote:  polar_coordinates(-1,-1) ==> [sqrt(2),(3/4)*π]
polar_coordinates([-1,-1]) ==> [sqrt(2),(-3/4)*π]

I was confused why those gave different results, but it's a typo. They give the same (expected) result: $$\begin{bmatrix} \sqrt 2& -\frac{3}{4}\ast\pi \end{bmatrix}$$.

— Ian Abbott
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