Measuring Angles in 360 Degrees: A Scientific Approach

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Discussion Overview

The discussion revolves around measuring angles in a 360-degree format rather than the traditional 180-degree format. Participants explore how to define a standard for determining whether an angle is over or under 180 degrees based on the positioning of two intersecting lines.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions the need for a "standard" to measure angles in a 360-degree system, suggesting that two lines meeting at a common point define angles that add up to 360 degrees.
  • Another participant expresses a desire for a calculation method that automatically returns angles in the 1-360 degree format, depending on the defined standard in the equation.
  • A participant illustrates the concept using a 90-degree angle, discussing how it could be interpreted as either 90 or 270 degrees based on the positioning of the lines.
  • One reply suggests using a Cartesian coordinate system to define the angles, indicating that the position of one line relative to the other can determine if the angle is less than or greater than 180 degrees.
  • Another participant mentions the "Cast Rule" for measuring angles, providing a method involving trigonometric functions to derive angle values.

Areas of Agreement / Disagreement

Participants express varying degrees of understanding and clarity regarding the original question. There is no consensus on how to approach the problem, and multiple interpretations of the angle measurement method are presented.

Contextual Notes

Some participants express confusion about the question's relevance and complexity, indicating that the discussion may depend on specific definitions and assumptions that remain unresolved.

Who May Find This Useful

This discussion may be of interest to individuals exploring geometric concepts, trigonometry, or those seeking methods for measuring angles in non-standard formats.

Jake
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Hi all,

This is a weird question,

I want to measure angles in terms of 360 degrees and not 180. The two lines will share a common point such that Line A ends at the point where Line B begins.

In order to do this don't you need to define some sort of "standard" so that you can know whether an angle is over or under the 180 mark?

Anyway, how could I do this?

(searched google and whatnot but found nothing. Perhaps there's some special keyword to use?)

Thanks a lot! :)
 
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Jake said:
Hi all,

This is a weird question,

I want to measure angles in terms of 360 degrees and not 180. The two lines will share a common point such that Line A ends at the point where Line B begins.

In order to do this don't you need to define some sort of "standard" so that you can know whether an angle is over or under the 180 mark?

Anyway, how could I do this?

(searched google and whatnot but found nothing. Perhaps there's some special keyword to use?)

Thanks a lot! :)
Two lines meeting at a common point define two angles which add up to 360 deg. Pick one.
 
Hi Mathman,

I don't want to have to pick one or the other. I want the calculation to automatically return the result in the 1-360 degree format, based on some standard I set in the equation.

Picture two lines at a 90 degree angle. That can either be considered a 90 degree angle or 270 (obviously). But I want to somehow "set" the equation so that when line A is "on one side" of Line B, the angle will be under 180, and if its on the "other side" the angle will be over 180.

Am I making any sense?

Thanks again :)
 
Last edited:
Jake said:
Hi Mathman,

I don't want to have to pick one or the other. I want the calculation to automatically return the result in the 1-360 degree format, based on some standard I set in the equation.

Picture two lines at a 90 degree angle. That can either be considered a 90 degree angle or 270 (obviously). But I want to somehow "set" the equation so that when line A is "on one side" of Line B, the angle will be under 180, and if its on the "other side" the angle will be over 180.

Am I making any sense?

Thanks again :)

this is a confusing question!
theatha=90
...B|A
t=180.|
_____ |______ Theatha=0 or 360 (after full revolution)
...|
...|
...|
t=270

Like this??

Notes: Theatha= Angle Value

What Topic is this??
What Level? I can only help you A level Downwards...
hope i donno this kinda helps..

In terms of 360 what do you mean Theatha/360 ? That doesn return the angle erm.

If Line A and Line B are opposite to each other won't that mean that its

Theatha=90
Alpha=180

Theatha+Alpha=270.

Why is this even relevant to you ...

I'm sorry I just don't understand the question.asked..jus trying to help

You can always use the Cast Rule to Measure Angles.
Lets say of Cos(Thetha)=1/2
SIN...|...ALL
...|...
...|...
_____ |______
...|...
...|...
TAN...|...COS
Make Lines from (0,0) obtuse outwards ...on ALL and COS.
Find Thetha by using calculator Cos^-1 (1/2) = 60 Degrees.
then measure First is ..60 and the second is 360-60 = 300 Degrees.
Hence Thetha =60,300 . ect ..

You can measure angles using Thetha = +/-PV +360n but i donno what level you're doing..
its perplexing ..just can't understand it.
 
Last edited:
Hi Phy, Thanks for following up.

Let me illustrate my point clearer by using a simple pictured In the Attachment below.

As you can see I have a blue and orange area, and two lines, A and B. I want to define the equation such that I will 'pick' an arbitrary 'side' of line A, such that when line B falls on one side it will be less than 180 degrees and on the other greater than 180.
 

Attachments

  • Line Diagram.jpg
    Line Diagram.jpg
    6.8 KB · Views: 506
Looking at the diagram, it looks like you should place the A,B common point at the origin of a standard cartesian coordinate system and make A lie along the y-axis in the positive direction. Then if the x component of B is positive the angle is less than 180 deg., if negative the angle will be greater than 180 deg.
 
Hey mathman, thanks, I see where that is going and think I can make something work :D
 

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