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.
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)