Radius Vector, Tangent Angle
Let P (r, ) be any point on the curve r = ƒ(). The angle between the radius vector and the tangent TPT’ at P is usually denoted by Ø.
Let ∠XTP = ψ. Then tan ψ = dy/dx (1)
It is clear from the figure that ψ = + Ø (2)
If (x, y) are the cartesian co-ordinates of P, then
x = r cos ,
y = r sin
or, x = ƒ() cos ,
y = ƒ() sin
These may be regarded as parametric equations of the given curve, being the parameter. We have
dx/d = ƒ’ () cos - ƒ() sin
dx/d = ƒ’ () cos + ƒ() sin
Dividing the numerator and the denominator by ƒ’ () cos and using (1), we obtain
from (2), we get
It follows from (3) and (4) that
Services: - Radius Vector, Tangent Angle Homework | Radius Vector, Tangent Angle Homework Help | Radius Vector, Tangent Angle Homework Help Services | Live Radius Vector, Tangent Angle Homework Help | Radius Vector, Tangent Angle Homework Tutors | Online Radius Vector, Tangent Angle Homework Help | Radius Vector, Tangent Angle Tutors | Online Radius Vector, Tangent Angle Tutors | Radius Vector, Tangent Angle Homework Services | Radius Vector, Tangent Angle