If x and y are connected parametrically by the equations given in without eliminating the parameter, Find dy/dx.
x = a (cos θ + θ sin θ), y = a (sin θ – θ cos θ)

Question

If x and y are connected parametrically by the equations given in without eliminating the parameter, Find dy/dx. x = a (cos θ + θ sin θ), y = a (sin θ – θ cos θ)

Philoid · Accepted Answer

It is given that

x = a (cos θ + θ sin θ), y = a (sin θ – θ cos θ)

Then, we have

= a[-sinθ + θcosθ + sinθ]

= aθcosθ…………………… (1)

= a[cosθ + θsinθ - cosθ]

= aθsinθ…………………… (2)

From (1) and (2) we get,

= tanθ

Hence, the value of is tanθ

If x and y are connected parametrically by the equations given in without eliminating the parameter, Find dy/dx.x = a (cos θ + θ sin θ), y = a (sin θ – θ cos θ)

If x and y are connected parametrically by the equations given in without eliminating the parameter, Find dy/dx.
x = a (cos θ + θ sin θ), y = a (sin θ – θ cos θ)