Angles - why in radians instead of in degrees?

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Discussion Overview

The discussion revolves around the preference for using radians over degrees in electrical engineering contexts, exploring the reasons behind this choice and its implications for equations and calculations.

Discussion Character

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

Main Points Raised

  • Some participants suggest that radians are more natural for solving various electrical problems.
  • One participant notes that using radians simplifies equations, such as the arc length of a circle segment being equal to rθ.
  • Another participant emphasizes the importance of radians in differentiation, particularly in relation to trigonometric functions, stating that using degrees would introduce unnecessary constants in calculations.
  • A humorous remark is made about the educational aspect of learning both radians and degrees, implying a necessity for flexibility in switching between these units.

Areas of Agreement / Disagreement

Participants express various viewpoints on the advantages of using radians, but there is no consensus on a singular reason or model for why radians are preferred over degrees.

Contextual Notes

Some arguments depend on the definitions of angles and the mathematical principles involved, particularly in differentiation and integration of trigonometric functions. The discussion does not resolve these complexities.

amaresh92
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angles -- why in radians instead of in degrees?

greetings,

why all the angle in electrical is represented in radian instead in degree?
advanced thanks
 
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amaresh92 said:
greetings,

why all the angle in electrical is represented in radian instead in degree?
advanced thanks

Can you think of some reasons? What kind of equations do we typically use in EE?
 


amaresh92 said:
greetings,

why all the angle in electrical is represented in radian instead in degree?
It makes for simpler equations,
e.g., the arc length of a circle segment = r.θ[/size][/color]
 


berkeman said:
Can you think of some reasons? What kind of equations do we typically use in EE?

equations normally involves both magnitude and phase.
 


It seems quite arbitrary until you look into the basic principles of differentiation. You are looking to find the slope of a curve, a sine wave say, by making a small triangle and working out the lengths of the sides. Then you find the value as the triangle size approaches zero. The simple answer that d(Sin θ)/dθ = Cos θ relies on using radians to measure that angle.
"www.mash.dept.shef.ac.uk/Resources/sincosfirstprinciples.pdf" presents it more or less as I remember being taught in medieval times by dear old Mr Worthington. Half way through, they make the point that the angle is in radians. If you don't measure the angle in radians, every time you differentiate or integrate a trig function, you get a bizarre constant, depending on which angle units you chose.
The inhabitants of Planet Zog, who use 413 zogdegrees in their circles will also be using radians and not zogdegrees for this reason.
 
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If they didn't use both angles and radians...they wouldn't have anything to test you on in school...lol

Seriously, you need to be able to "snap" back and forth from angles to radians and then snap over to frequency...then snap over to the period. You will always be going back and forth between these things. Learn them now and embrace them. They all have their purposes.
 

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