Question

Find $\frac{dy}{dx}$, if x = a(θ - sin θ), y = a(1 - cos θ)

Answer 1

i hope it is correct

Answer 2

Answer:

$\dfrac {sin\theta}{1 - cos\theta}$

Step-by-step explanation:

Given:

$x = a(\theta - sin\theta)$

Now differentiate x with respect to $\theta$

$\dfrac{dx}{d\theta }= \dfrac {d\ a(\theta - sin\theta))}{d\theta}\\\\\dfrac{dx}{d\theta}= a(1 - cos\theta)...... (1)$

$y = a(1 - cos\theta)$

Now differentiate y with respect to $\theta$

$\dfrac{dy}{d\theta }= \dfrac {d\ a(1 - cos\theta))}{d\theta}\\\\\dfrac{dy}{d\theta }= a(0 - (-sin\theta))\\\\\dfrac{dy}{d\theta }= asin\theta..... (2)$

divide equation (2) by (1) to find dy/dx

$\dfrac{\dfrac {dy}{d\theta}}{\dfrac {dx}{d\theta}} = \dfrac{asin\theta}{a(1 - cos\theta)}\\\\\dfrac {dy}{dx} = \dfrac {sin\theta}{1 - cos\theta}$