Working with degrees instead of radians

In summary, the derivative of Sin[x] with respect to x is Cos[x] when x is measured in radians. The formula Sin[x degrees] = Sin[2π/360 x radians] can be used to calculate the derivative of Sin[x degrees] with respect to x. However, using degrees instead of radians can make calculus difficult due to the pi/180 nuisance factor in all derivatives of trigonometric functions.
  • #1
cornelius bay
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Homework Statement



If x is measured in radians, then the derivative of Sin[x] with respect to x is Cos[x].

Use the formula Sin [x degrees] = Sin [2π/360 x radians]
to calculate the derivative of Sin [x degrees] with respect to x.

Why does the resulting formula make calculus difficult if you insist on working with degrees instead of radians?

Thanks for any help you can offer!

Homework Equations


y = sin [πx/180]
y' = 1/180 * π * cos[πx/180]

The Attempt at a Solution


I don't understand the "Why does the resulting formula make calculus difficult if you insist on working with degrees instead of radians?" question.
 
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  • #2
Don't you think that having a pi/180 nuisance factor in all derivatives of the trig functions qualifies as a reason?
 

What is the difference between degrees and radians?

Degrees and radians are units of measurement for angles. Degrees are commonly used in everyday life and are based on dividing a circle into 360 equal parts. Radians, on the other hand, are used more frequently in mathematics and science and are based on dividing a circle into 2π (approximately 6.28) equal parts.

Why do scientists prefer to work with radians instead of degrees?

Radians are preferred by scientists because they are a more natural unit of measurement for angles in mathematical calculations. Radians simplify many calculations involving trigonometric functions and make it easier to work with the properties of circles and spheres.

Is there a conversion formula for degrees to radians?

Yes, the conversion formula for degrees to radians is: radians = degrees x π/180. This means that 180 degrees is equal to π radians, or 1 degree is equal to π/180 radians.

How do radians and degrees relate to each other?

Radians and degrees are both units of measurement for angles and can be converted to each other using the conversion formula mentioned above. One full rotation in radians is equal to 2π, which is equivalent to 360 degrees.

Can I use degrees and radians interchangeably in all calculations?

No, degrees and radians should not be used interchangeably in calculations. While they are convertible, they represent two different units of measurement and have different properties. It is important to use the appropriate unit for the specific calculation being performed.

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