Find the equations of the tangent and the normal to the curve

Given: x = 1 – cos θ and y = θ – sin θ

To find: equations of the tangent and the normal to the curve

Formula used:

The equation of tangent is:

The equation of normal is:

Therefore,

x = 1 – cos θ and y = θ – sin θ

Differentiating both with respect to θ:

Now,

At, :

The equation of tangent is:

The equation of normal is: