SUMMARY
The discussion focuses on finding the gradient of the angle θ defined by the expression cosθ = (a·b)/(ab) without using differentials of arccos. The user specifically seeks methods applicable for angles between 60 and 100 degrees, ruling out small angle approximations. Participants confirm the objective is to compute ∇rθ, emphasizing the need for alternative approaches to traditional calculus methods.
PREREQUISITES
- Understanding of vector dot product and its geometric interpretation
- Familiarity with gradient notation and vector calculus
- Knowledge of trigonometric functions and their derivatives
- Basic concepts of multivariable calculus
NEXT STEPS
- Research methods for calculating gradients in vector fields
- Study the relationship between angles and gradients in vector calculus
- Explore alternative trigonometric identities for angles beyond small approximations
- Learn about the implications of using implicit differentiation in vector calculus
USEFUL FOR
Students and professionals in mathematics, physics, and engineering who require a deeper understanding of vector calculus and gradient computations without relying on standard differential methods.