Radians vs Degrees: When to Use in Calculus & Physics

In summary, the conversation discusses the use of radians versus degrees in trigonometric calculations and how they are used in different contexts. The speakers also mention the preference for radians in mathematical functions and the use of calculators by engineers. Ultimately, it is important to use the appropriate unit (radians or degrees) depending on the given problem or question.
  • #1
Llama77
113
0
So I have a few different calculators I use. I am currently in a Calculus 1 and Physics 1 course. Both for engineers.

As am example of what I am trying to explain, such as my physics HW It asked me to calculate the magnitude of the Vectors A+B+C. I do so and It worked fine, I did this is radians, But then it asked me for the degrees of the added vectors and I gave it the answer but it said i was wrong. Now my calculation were right, all except I think i should have been in degree's rather than radians. When i redid all the math in degrees the degrees section was now correct.

So I am looking for some advice on knowing which to use, as I have been told by my calc professors that Degree's is Barbaric or something to that nature.


Thank you.
 
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  • #2
What's barbaric about a quantitiy proportional to radians??
Poor degrees! I'll rush to their defense any day..
 
  • #3
You use several different calculators? T-83 and beyond can switch from degrees to radians.

Anyway, the best way to know which to use is by context. If the variables in the problem deal with degrees, use degrees, if they are just constants, use radians.
 
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  • #4
radians are clearly the best abstractly, but degrees are the most understandable. i.e. everyone in my generation knows what 90 degrees means, and we do not all know quickly what pi/2 radians means, much less 2 radians.

measuring angles in degrees is sort of like meaasuring lengths in cubits.
 
  • #5
so if the problem is going to ask for degrees or had degrees in it then I should just stick with degrees for ?
 
  • #6
Indeed you should!

You should always answer the question, whatever the question is.
 
  • #7
mathwonk said:
radians are clearly the best abstractly
Well I know how it is derived but still it is not clear to me at all that it is "clearly the best". :smile:
Especially not abstractly!

In abstract terms I would actually prefer: [itex] 1c \iff 360^\circ \iff 2\pi rad[/itex],
where c stands for circumnavigation. :smile:

Anyway it is just a convention and radians seems to be the clear winner.
 
  • #8
Llama77 said:
So I have a few different calculators I use. I am currently in a Calculus 1 and Physics 1 course. Both for engineers.

As am example of what I am trying to explain, such as my physics HW It asked me to calculate the magnitude of the Vectors A+B+C. I do so and It worked fine, I did this is radians, But then it asked me for the degrees of the added vectors and I gave it the answer but it said i was wrong. Now my calculation were right, all except I think i should have been in degree's rather than radians. When i redid all the math in degrees the degrees section was now correct.

So I am looking for some advice on knowing which to use, as I have been told by my calc professors that Degree's is Barbaric or something to that nature.


Thank you.

Are you sure that you entered in the right quantity when you were doing your trig calculations. For example, if you put a number into a trig function, and your calculator thinks it's operating in radians when you were using degrees, then you'll obviously get a wrong answer.

Anyway, to answer your question, I think you'll find that both degrees and radians are used in physics. It really depends on context. For example, when talking about the phase of an AC signal or the angular displacement of a rotating object, we'll typically use radians. When we talk about the angle at which a projectile is launched, degrees usually win out. To put it simply, degrees are easier to visualize, but radians are more elegant and easier to work with mathematically.

Whatever you do, always use radians when you're taking a derivative of a trig function!
 
  • #9
The functions used in mathematics, as opposed to calculations in, say, physics have no "units". If f(t)= t2, neither the t nor f(t) are measured in feet or meters- they are just numbers.
Similarly, in the functions sin(t) and cos(t), x has no units- in particular they are not measured in degrees or radians.

In fact, one definition of sign and cosine widely used in calculus or pre-calculus measures the variable t around the circumference of a unit circle. It is not an angle and so cannot be measured in degrees or radians.

Of course, calculators are designed by engineers, not mathematicians, and they think of sine and cosine in terms of angles (look at the "phase angle" in waves where there are no angles at all!). The radian measure of an angle is really the distance around the circumference of a unit circle subtended by that angle and so corresponds to the "circle" definition. The "x" in sin(x) or cos(x) corresponds to radian measure of an angle. That is, I am sure, what your math professors were telling you (did they really use the word "barbaric"??).

In your vector problem, you are doing an application of mathematics in which there really are angles so that either radians or degrees (or even "grads"- one hundredth of a right angle) would be appropriate. If "then it asked me for the degrees of the added vectors", then it would be foolish of you to use anything other than degrees!
 
  • #10
I'm still unsure about, when to use radians or degress in my calculator.

Could anyone give an example of both cases?
What should I use, if I'm to find sin(2)?
Why is that sometimes the difference in radians or degrees do not matter?

Thank you.
 
  • #11
knowNothing23 said:
I'm still unsure about, when to use radians or degress in my calculator.

Could anyone give an example of both cases?
What should I use, if I'm to find sin(2)?
Why is that sometimes the difference in radians or degrees do not matter?

Thank you.

What does "2" measure? Use the unit in your calculator process. If the "2" measures degrees, then set your calculator for degrees. If the "2" measures radians, then set the calculator for radians. If you do not want to reset your calculator between degrees and radians, then simply use the ratio of 360 degrees equals 2∏ radians.
 
  • #12
What if there's no indication of what's required? Neither radians or degrees?
 
  • #13
Do the problem in the angle measure of your choise. Give the answer in both.
 
  • #14
knowNothing23 said:
What if there's no indication of what's required? Neither radians or degrees?

Then the question was not written right and is meaningless, unless you know in advance which unit is intended.

Integral said:
Do the problem in the angle measure of your choise. Give the answer in both.

That's one approach, but the problem description needs to be sufficiently given.
 
  • #15
As I said in my previous post, when a trig function appears purely as a "function", without reference to an angle, then the units should be "radians" (strictly speaking it has no units but to put it into a calculator, you must use radians).

I agree with symbolipoint that, if a problem deals with angles, then the problem should state whether it is measured in degrees or radians. But if you simply have sine or cosine functions, without reference to angles, you can assume radians are intended.
 

1. What are radians and degrees?

Radians and degrees are two units of measurement used to measure angles. Degrees are commonly used in everyday life, while radians are often used in mathematics and physics.

2. When should I use radians and when should I use degrees?

In calculus and physics, radians are typically used because they are a more natural unit for measuring angles in mathematical equations. However, in many practical applications, such as navigation or construction, degrees may be more convenient to use.

3. How do you convert between radians and degrees?

There are two common ways to convert between radians and degrees. One way is to use the conversion formula: 1 radian = 180/π degrees. Another way is to use the fact that a full circle is 360 degrees or 2π radians, so you can convert by multiplying or dividing by π/180.

4. Can you use both radians and degrees in the same problem?

Yes, you can use both radians and degrees in the same problem, but it is important to be consistent and convert between the two units if necessary. It is often easier to stick with one unit throughout the problem to avoid confusion.

5. Are radians and degrees interchangeable?

No, radians and degrees are not interchangeable. They represent different units of measurement for angles. However, some calculators and software programs may allow you to switch between the two units for convenience.

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