If x = a sin theta and y = b cos theta,then f | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given $x = a \sin 	heta$ and $y = b \cos 	heta$. First,find the derivatives with respect to $	heta$: $\frac{dx}{d	heta} = a \cos 	heta$ and $

Vedclass · Accepted Answer

$-\frac{b}{a^2} \sec^3 	heta$

Vedclass · Answer

(C) Given $x = a \sin 	heta$ and $y = b \cos 	heta$. First,find the derivatives with respect to $	heta$: $\frac{dx}{d	heta} = a \cos 	heta$ and $\frac{dy}{d	heta} = -b \sin 	heta$. Now,find $\frac{dy}{dx}$ using the chain rule: $\frac{dy}{dx} = \frac{dy/d	heta}{dx/d	heta} = \frac{-b \sin 	heta}{a \cos 	heta} = -\frac{b}{a} 	an 	heta$. Next,differentiate $\frac{dy}{dx}$ with respect to $x$: $\frac{d^2y}{dx^2} = \frac{d}{dx} \left( -\frac{b}{a} 	an 	heta ight) = -\frac{b}{a} \sec^2 	heta \cdot \frac{d	heta}{dx}$. Since $\frac{dx}{d	heta} = a \cos 	heta$,we have $\frac{d	heta}{dx} = \frac{1}{a \cos 	heta}$. Substituting this value: $\frac{d^2y}{dx^2} = -\frac{b}{a} \sec^2 	heta \cdot \frac{1}{a \cos 	heta} = -\frac{b}{a^2} \sec^3 	heta$.

If $x = a \sin \theta$ and $y = b \cos \theta$,then $\frac{d^2y}{dx^2}$ is

Similar Questions

If $x$ and $y$ are connected parametrically by the equations,without eliminating the parameter,find $\frac{dy}{dx}$ for $x = a \sec \theta$ and $y = b \tan \theta$.

If $\tan y = \frac{2t}{1 - t^2}$ and $\sin x = \frac{2t}{1 + t^2},$ then $\frac{dy}{dx} = $

If $x = a \cos^4 \theta$ and $y = a \sin^4 \theta$,then $\frac{dy}{dx}$ at $\theta = \frac{3\pi}{4}$ is

If $x = a(1 - \cos \theta)$ and $y = a(\theta + \sin \theta)$,then $\frac{dy}{dx} = $ . . . . . . .

If $x = a(\cos t + \log \tan \frac{t}{2})$ and $y = a \sin t$,then $\frac{dy}{dx} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module