What is the Negative of a Polar Coordinate?

[Physicist3]

Hi,

Say I have a variable 'x' which has the polar value 10@-75°, would '-x' be -10@+75° or 10@+75° as I am a touch confused as to which bit I have to invert

 

[slider142]

Hi,

Say I have a variable 'x' which has the polar value 10@-75°, would '-x' be -10@+75° or 10@+75° as I am a touch confused as to which bit I have to invert

The notation "-x" usually refers to the additive inverse of x. That is, we want x + (-x) = 0. Therefore, if you are using the usual Euclidean notion of vector addition (the parallelogram law, equivalent to the addition of Cartesian components), you must find the polar components of the vector whose addition to x will yield the additive identity: the 0 vector. In the vectors of Euclidean geometry, this is the vector that points in opposite direction to x, but with equal magnitude. Thus, it is the reflection of x through the origin (if one attaches the tail of x to the origin). Attached is an example of the geometric viewpoint. Do you see which vector that should be for your particular case ? After you find it geometrically, then you would find its polar components.
Of course, if you are using a different notion of vector addition, then your result will vary. In that case, you would have to describe the context of your application.

 

[mathman]

Hi,

Say I have a variable 'x' which has the polar value 10@-75°, would '-x' be -10@+75° or 10@+75° as I am a touch confused as to which bit I have to invert

In polar coordinates x and -x have the same magnitude and have angles which differ by 180 deg. In your example -x is 10@105 deg.