Question

find the angle between radius vector and tangent r=a(1+sinθ) ​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Ф = π/4 + Θ/2 is the correct answer

Given:

r = a(1+ sinΘ)

To find:

the angle between radius vector and tangent r=a(1+sinθ) ​

solution:

r=a(1+sinθ) ​

(1/r)dr/dΘ = cosΘ/(1+sinΘ)

rdΘ/dr = 1 + sinΘ/ cosΘ

tanΨ = (cos²Θ/2 + sin²Θ/2 + 2sinΘ/2 . cosΘ/2)/ (cos²Θ/2 - sin²Θ/2)

= (cosΘ/2 + sinΘ/2)²/((cosΘ/2 - sinΘ/2) . (cosΘ/2 + sinΘ/2))

= 1 + tanΘ/2 / 1 - tanΘ/2

= tan( π/4 + Θ/2)

hence, Ψ = π/4 + Θ/2 is the correct answer