Explore BrainMass

Explore BrainMass

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

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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.

    © BrainMass Inc. brainmass.com February 24, 2021, 2:29 pm ad1c9bdddf


    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 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.