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Question
If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.
x = sin t, y = cos 2t
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Solution
Given, x = sin t and y = cos 2t
Differentiating both sides with respect to t,
`dx/dt = d/dt (sin t)`
= cos t
And `dy/dt = d/dt (cos 2t)`
= `-sin 2t d/dt (2t)`
= −2 sin 2t
`dy/dx = (dy/dt)/(dx/dt)`
= `(-2 sin 2t)/(cos t)`
sin (2t) = 2 sin t cos t
`dy/dx = (-2(2 sin t cos t))/(cos t)`
`dy/dx = (-4 sin t cos t)/(cos t)`
`dy/dx` = −4 sin t
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