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Severity: Notice

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Sponsor Area

Continuity And Differentiability

Question

$If space space straight x equals straight a left parenthesis 1 minus cosθ right parenthesis comma space straight y equals straight a left parenthesis 1 plus sinθ right parenthesis comma space find dy over dx comma$

Solution

space straight x equals straight a left parenthesis 1 minus cosθ right parenthesis space rightwards double arrow dx over dθ equals straight a space sinθ space straight y equals straight a left parenthesis 1 plus sinθ right parenthesis space rightwards double arrow space dy over dθ equals straight a space cosθ Now space dy over dθ equals fraction numerator begin display style dy over dθ end style over denominator begin display style dx over dθ end style end fraction equals fraction numerator straight a space cosθ over denominator straight a space sinθ end fraction equals cotθ