Question

Find dy/dx, when


x = a cos3 theta, y = a sin3 theta


answer: - tan theta

Answer 1

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Answer 2

Answer:

$\frac{dy}{dx}$ = -tanθ

Step-by-step explanation:

Given,

x = acos³θ

y = asin³θ

To find,

$\frac{dy}{dx}$

Solution:

$\frac{dy}{dx}$ = $\frac{dy}{d\theta} X\frac{dx}{d\theta}$

y = asin³θ

$\frac{dy}{d\theta}$ = 3asin²θcosθ

$\frac{dx}{d\theta}$ = 3acos²θ×-sinθ

$\frac{d\theta}{dx} = \frac{-1}{3acos^2\theta sin\theta}$

$\frac{dy}{dx}$ = $\frac{dy}{d\theta} X\frac{dx}{d\theta}$

=  3asin²θcosθ × $\frac{-1}{3acos^2\theta sin\theta}$

= $\frac{-sin\theta}{cos\theta}$

= -tanθ

$\frac{dy}{dx}$ = -tanθ

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