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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`
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