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# If X = A (2θ – Sin 2θ) And Y = A (1 – Cos 2θ), Find Dy/Dx When Theta = Pi/3 - CBSE (Science) Class 12 - Mathematics

ConceptDerivatives of Functions in Parametric Forms

#### Question

If x = a (2θ – sin 2θ) and y = a (1 – cos 2θ), find dy/dx when theta = pi/3

#### Solution

Applying parametric differentiation

dx/(d theta) = 2a - 2acos2theta

dy/(d theta) = 0 + 2asin 2theta

dy/dx = dy/(d theta) xx (d theta)/dx = (sin 2 theta)/(1-cos 2 theta)

Now putting the value of theta = pi/3

dy/dx|_(theta = pi/3) =  (sin 2(pi/3))/(1-cos2(pi/3))

= (sqrt3/2)/(1+ 1/2)

= (sqrt3/2)/(3/2) = 1/sqrt3

So dy/dx is 1/sqrt3 at theta = pi/3

Is there an error in this question or solution?

#### APPEARS IN

Solution If X = A (2θ – Sin 2θ) And Y = A (1 – Cos 2θ), Find Dy/Dx When Theta = Pi/3 Concept: Derivatives of Functions in Parametric Forms.
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