Angles - why in radians instead of in degrees?

In summary, angles are more natural to use in equations when solving electrical problems because they rely on the principles of differentiation and frequency more than degrees do.
  • #1
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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  • #3


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?
 
  • #4


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
 
  • #5


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.
 
  • #6


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.
 
Last edited by a moderator:
  • #7


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.
 

1. Why do we use radians instead of degrees to measure angles?

Radians are a more natural and convenient unit for measuring angles in many mathematical and scientific applications. They have a direct relationship to the properties of circles and are useful for calculus and trigonometry calculations. Additionally, radians allow for more accurate and precise measurements compared to degrees.

2. How do radians and degrees relate to each other?

Radians and degrees are two different units for measuring angles. One full rotation around a circle is equal to 360 degrees or 2π radians. This means that 180 degrees is equivalent to π radians, 90 degrees is equal to π/2 radians, and so on.

3. Can you convert radians to degrees and vice versa?

Yes, radians and degrees can be converted using the formulas: radians = (degrees * π)/180 and degrees = (radians * 180)/π. Many calculators and mathematical software also have built-in functions for converting between radians and degrees.

4. Are there any advantages to using radians over degrees?

Yes, there are several advantages to using radians over degrees. One is that they make calculations in calculus and trigonometry simpler and more elegant. Additionally, radians allow for more accurate and precise measurements, especially when working with small angles. They also have a direct relationship to the properties of circles, making them useful in many geometric and physics applications.

5. Is it necessary to use radians in all mathematical and scientific applications?

No, radians are not necessary in all applications, and degrees are still commonly used in many fields. However, radians are the preferred unit for most mathematical and scientific calculations, as they offer several advantages over degrees. It ultimately depends on the specific application and personal preference.

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