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

Similar Questions

The rate of change of $\sqrt{x^2+16}$ with respect to $\frac{x}{x-1}$ at $x=5$ is

If $x = \sin t$ and $y = \sin pt$,then the value of $(1 - x^2) \frac{d^2 y}{d x^2} - x \frac{d y}{d x} + p^2 y =$

If $x = 2 \sin \theta - \sin 2 \theta$ and $y = 2 \cos \theta - \cos 2 \theta$ where $\theta \in [0, 2 \pi]$,then find the value of $\frac{d^{2} y}{dx^{2}}$ at $\theta = \pi$.

If $x = \sqrt{a^{\sin^{-1} t}}$ and $y = \sqrt{a^{\cos^{-1} t}}$,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

Vedclass Test Series

Exam Paper Generator

Online Exam Module