Working with degrees instead of radians

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SUMMARY

The discussion focuses on the challenges of calculating derivatives of trigonometric functions when using degrees instead of radians. The derivative of Sin[x degrees] is derived as y' = (π/180) * Cos[πx/180], introducing a constant factor that complicates calculus operations. This pi/180 factor is identified as a significant nuisance, making calculations less straightforward compared to using radians. The consensus is that working in radians simplifies the process and avoids unnecessary complexity in derivatives.

PREREQUISITES
  • Understanding of trigonometric functions and their derivatives
  • Familiarity with calculus concepts, particularly differentiation
  • Knowledge of the relationship between degrees and radians
  • Basic algebra skills for manipulating equations
NEXT STEPS
  • Study the implications of using radians in calculus, particularly in trigonometric derivatives
  • Learn about the unit circle and its role in converting between degrees and radians
  • Explore the application of the chain rule in differentiation of trigonometric functions
  • Investigate the historical context and reasons for the preference of radians in mathematical analysis
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Students studying calculus, educators teaching trigonometry, and anyone interested in understanding the mathematical implications of using degrees versus radians in calculus.

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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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Don't you think that having a pi/180 nuisance factor in all derivatives of the trig functions qualifies as a reason?
 

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