Differentiate the law of Cosine

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SUMMARY

The law of cosines is expressed as R² = h² + r² - 2hr cos(θ), where θ is the angle opposite side R. To differentiate this equation, the user sets up the equation r² - 2hr cos(θ) + (h² - R²) = 0 and derives the expression 2r·dr - 2h cos(θ)·dr + (h² - R²) = 0. The discussion concludes with the user successfully resolving their query regarding the differentiation process.

PREREQUISITES
  • Understanding of trigonometric identities, specifically the law of cosines.
  • Familiarity with calculus concepts, particularly differentiation.
  • Knowledge of implicit differentiation techniques.
  • Basic understanding of angular measurements in radians.
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  • Study implicit differentiation methods in calculus.
  • Explore applications of the law of cosines in physics and engineering.
  • Learn about the relationship between angular velocity and differentiation.
  • Investigate advanced trigonometric identities and their proofs.
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Students and professionals in mathematics, physics, and engineering who are looking to deepen their understanding of trigonometric differentiation and its applications.

ryank614
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It is a simple math question, but I am stuck.

The law of cosines is

R^2=h^2 + r^2 - 2 h r cos (theta). Theta is of course the angle facing R.

To differentiate, I first set

r^2 - 2hr cos\Theta+ (h^2-R^2) = 0

2 r \dot{}r - 2 h cos\Theta \dot{}r + (h^2-R^2) = 0.

Is there any way to put h^2-R^2 in terms of \dot{}\theta or d\theta/dt
 
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Arr, nevermind. I got it.
 

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