Find ds/d? for the curves : r2 = a2cos2? etc.,
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Tangent and Normal (II)
(Differential Calculus)
Find ds/d? for the curves : (a) r2 = a2cos2? (b) rn = ancosn?
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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.
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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
= ...
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- MSc, Kanpur University
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