Find the equation of the tangent and the normal to the following curves at the indicated points:
x = θ + sin θ, y = 1 + cos θ at θ = π/2.

Question

Find the equation of the tangent and the normal to the following curves at the indicated points:x = θ + sin θ, y = 1 + cos θ at θ = π/2.

Philoid · Accepted Answer

finding slope of the tangent by differentiating x and y with respect to theta

Dividing both the above equations

m(tangent) at theta ( ) = – 1

normal is perpendicular to tangent so, m₁m₂ = – 1

m(normal) at theta ( ) = 1

equation of tangent is given by y – y₁ = m(tangent)(x – x₁)

equation of normal is given by y – y₁ = m(normal)(x – x₁)