If $x=a(2\theta-\sin 2\theta)$ and $y=a(1-\cos 2\theta)$, find $\dfrac{dy}{dx}$ when $\theta=\dfrac{\pi}{3}$.

CBSE Class 12 · 2018 · DifferentiationLong Answer

x = a (2 θ - sin 2 θ)

and

y = a (1 - cos 2 θ)

, find

\frac{d y}{d x}

when

θ = \frac{π}{3}

Answer: $\frac{1}{3}$

Differentiate w.r.t.

θ

\frac{d x}{d θ} = a (2 - 2 cos 2 θ) = 4 a sin^{2} θ, \frac{d y}{d θ} = 2 a sin 2 θ = 4 a sin θ cos θ

Divide:

\frac{d y}{d x} = \frac{4 a sin θ cos θ}{4 a sin ^{2} θ} = cot θ

θ = \frac{π}{3}

cot \frac{π}{3} = \frac{1}{3}

\frac{d y}{d x}_{θ = π /3} = \frac{1}{3}

CBSE Class 12 Board · 2018 · Subjective