Question

$Find space dy over dx when space straight x equals straight a left parenthesis straight ө minus sinө right parenthesis space comma straight y equals straight a left parenthesis 1 plus cosө right parenthesis$

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Solution

space space space space space space straight x equals straight a left parenthesis straight ө minus sinө right parenthesis comma space straight y equals straight a left parenthesis 1 plus cosө right parenthesis dx over dθ equals straight a left parenthesis 1 minus cosθ right parenthesis dy over dθ equals straight a left parenthesis 0 minus sinθ right parenthesis dy over dx 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 negative asinθ over denominator straight a left parenthesis 1 minus cosθ right parenthesis end fraction equals negative fraction numerator 2 sin begin display style straight theta over 2 end style cos begin display style straight theta over 2 end style over denominator 2 sin squared begin display style straight theta over 2 end style end fraction equals negative cot straight theta over 2

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