Find frac{dy}{dx},if x = a cos theta and y = | vedclass

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(A) Given the parametric equations:$x = a \cos 	heta$$y = a \sin 	heta$First,differentiate $x$ with respect to $	heta$:$\frac{dx}{d	heta} = \frac{

Vedclass · Accepted Answer

$-\cot 	heta$

Vedclass · Answer

(A) Given the parametric equations:$x = a \cos 	heta$$y = a \sin 	heta$First,differentiate $x$ with respect to $	heta$:$\frac{dx}{d	heta} = \frac{d}{d	heta}(a \cos 	heta) = -a \sin 	heta$Next,differentiate $y$ with respect to $	heta$:$\frac{dy}{d	heta} = \frac{d}{d	heta}(a \sin 	heta) = a \cos 	heta$Using the chain rule for parametric differentiation:$\frac{dy}{dx} = \frac{\frac{dy}{d	heta}}{\frac{dx}{d	heta}}$Substitute the values:$\frac{dy}{dx} = \frac{a \cos 	heta}{-a \sin 	heta}$Simplify the expression:$\frac{dy}{dx} = -\frac{\cos 	heta}{\sin 	heta} = -\cot 	heta$

Find $\frac{dy}{dx}$,if $x = a \cos \theta$ and $y = a \sin \theta$.

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