Derivative of (4995)/(1+.12cosθ) with θ = 120° - Simple Calculus Problem

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SUMMARY

The derivative of the function (4995)/(1 + 0.12cosθ) when θ = 120° was incorrectly calculated due to the use of degrees instead of radians. The correct approach involves using the derivative formula for the quotient and ensuring that angles are in radians. The expected result is approximately 10.253, contrasting with the erroneous calculation of about 587.478. This highlights the importance of angle measurement in calculus.

PREREQUISITES
  • Understanding of calculus derivatives, specifically the quotient rule.
  • Familiarity with trigonometric functions and their derivatives.
  • Knowledge of angle measurement in radians versus degrees.
  • Basic proficiency in using scientific calculators for trigonometric calculations.
NEXT STEPS
  • Review the quotient rule for derivatives in calculus.
  • Learn about converting degrees to radians in mathematical computations.
  • Practice calculating derivatives of trigonometric functions using radians.
  • Explore common mistakes in calculus related to angle measurement.
USEFUL FOR

Students beginning their studies in calculus, educators teaching derivative concepts, and anyone looking to clarify the importance of angle measurement in mathematical calculations.

LyleCoff
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Find the derivative of (4995)/(1+.12cosθ), when θ = 120°

My attempt:

d/dx [4995/(1+.12cosθ) = (4995)(-1)(1+.12cosθ)-2(.12)(-sinθ)

Letting θ = 120°...

= (4995)(-1)(1+.12(-1/2))-2(.12)(-[itex]\sqrt{3}[/itex]/2)


My calculator says that is about 587.478

But it's supposed to be about 10.253

I just started calculus, so I'm probably making some really basic mistake.
 
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Results are usually done in radians instead of degrees. Have you tried doing your

computation in radians?
 
To add to what Bacle2 has said, your standard formulas for the derivatives are correct only when the angles are given in radians.
 

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