Question

find the angle between radian vector and tangent of the following curves are? 2a÷r=1-cos theta .​

Answer 1

We have tan ϕ = r dθ/dr = r / dr/dθ

r = a (1 - cos θ) .

So dr/dθ = a sin θ .

Hence, tan ϕ = a (1 - cos θ) / (a sin θ)

= 2 sin^2 (θ/2) / (2 sin (θ/2) cos (θ/2) )

= tan (θ/2) .

So ϕ = θ/2 .