If x=a(theta+sin theta) and y=a(1-cos theta), | vedclass

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

Question

(B) Given $x = a(	heta + \sin 	heta)$ and $y = a(1 - \cos 	heta)$.First,differentiate $x$ with respect to $	heta$:$\frac{dx}{d	heta} = a(1 + \cos

Vedclass · Accepted Answer

$	an \frac{	heta}{2}$

Vedclass · Answer

(B) Given $x = a(	heta + \sin 	heta)$ and $y = a(1 - \cos 	heta)$.First,differentiate $x$ with respect to $	heta$:$\frac{dx}{d	heta} = a(1 + \cos 	heta)$.Next,differentiate $y$ with respect to $	heta$:$\frac{dy}{d	heta} = a(0 - (-\sin 	heta)) = a \sin 	heta$.Now,find $\frac{dy}{dx}$ using the chain rule:$\frac{dy}{dx} = \frac{dy/d	heta}{dx/d	heta} = \frac{a \sin 	heta}{a(1 + \cos 	heta)} = \frac{\sin 	heta}{1 + \cos 	heta}$.Using trigonometric identities $\sin 	heta = 2 \sin \frac{	heta}{2} \cos \frac{	heta}{2}$ and $1 + \cos 	heta = 2 \cos^2 \frac{	heta}{2}$:$\frac{dy}{dx} = \frac{2 \sin \frac{	heta}{2} \cos \frac{	heta}{2}}{2 \cos^2 \frac{	heta}{2}} = \frac{\sin \frac{	heta}{2}}{\cos \frac{	heta}{2}} = 	an \frac{	heta}{2}$.Thus,the correct option is $B$.

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

Similar Questions

If $x=a(t-\sin t)$ and $y=a(1+\cos t)$, then $\frac{d^2 y}{d x^2}=$

If $x = \sqrt{a^{\sin^{-1} t}}$ and $y = \sqrt{a^{\cos^{-1} t}},$ then $\frac{dy}{dx} = . . . . . .$

If $\cos (f(x))=\frac{1-x^2}{1+x^2}$ and $\tan (g(x))=\frac{3 x-x^3}{1-3 x^2}$,then $\frac{d f}{d g}=$

What is the slope of the tangent to the curve $x = t^2 + 3t - 8$ and $y = 2t^2 - 2t - 5$ at the point $t = 2$?

If $x=\sec \theta, y=\tan \theta$,then the value of $\frac{d^{2} y}{d x^{2}}$ at $\theta=\frac{\pi}{4}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module