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# 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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https://brainmass.com/math/calculus-and-analysis/find-ds-curves-r2-a2cos2-etc-23924

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Tangent and Normal (II)
(Differential Calculus)

Written by :- Thokchom Sarojkumar Sinha

Find ds/dÎ¸ for the curves : (a) r2 = a2cos2Î¸ (b) rn = ancosnÎ¸

Soluion :- (a) r2 = a2cos2Î¸

We know that ds/dÎ¸ = âˆš[r2 + (dr/dÎ¸)2] -------------------------(1)
Differentiating the equation r2 = a2cos2Î¸ with respect to 'Î¸' , we get
2r dr/dÎ¸ = a2 (- sin 2Î¸).2 = - 2a2sin2Î¸
or, dr/dÎ¸ = - a2sin2Î¸/r

Using this value in (1) , we get
ds/dÎ¸ = âˆš[r2 + (- a2sin2Î¸/r)2] = âˆš[r4 + a4sin22Î¸]/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.

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