Purchase Solution

Find ds/d? for the curves : r2 = a2cos2? etc.,

Not what you're looking for?

Ask Custom Question

Tangent and Normal (II)
(Differential Calculus)

Find ds/d? for the curves : (a) r2 = a2cos2? (b) rn = ancosn?

See attached file for full problem description.

Purchase this Solution

Solution Summary

This solution is comprised of a detailed explanation for finding ds/d? of curves.
It contains step-by-step explanation for finding ds/d? for the curves :
(a) r2 = a2cos2? (b) rn = ancosn?

Solution contains detailed step-by-step explanation.

Solution Preview

Please see the attached file.

Tangent and Normal (II)
(Differential Calculus)

Written by :- Thokchom Sarojkumar Sinha

Find ds/dθ for the curves : (a) r2 = a2cos2θ (b) rn = ancosnθ

Soluion :- (a) r2 = a2cos2θ

We know that ds/dθ = √[r2 + (dr/dθ)2] -------------------------(1)
Differentiating the equation r2 = a2cos2θ with respect to 'θ' , we get
2r dr/dθ = a2 (- sin 2θ).2 = - 2a2sin2θ
or, dr/dθ = - a2sin2θ/r

Using this value in (1) , we get
ds/dθ = √[r2 + (- a2sin2θ/r)2] = √[r4 + a4sin22θ]/r
= ...

Solution provided by:
  • BSc, Manipur University
  • MSc, Kanpur University
Recent Feedback
  • "Thanks this really helped."
  • "Sorry for the delay, I was unable to be online during the holiday. The post is very helpful."
  • "Very nice thank you"
  • "Thank you a million!!! Would happen to understand any of the other tensor problems i have posted???"
  • "You are awesome. Thank you"
Purchase this Solution

Free BrainMass Quizzes
Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.