Question

find the angle between the radius vector and the tangent of the following curves 2a/r=1-cosx​

Answer 1

Answer:

0 /2 is correct I think so

Answer 2

Answer:

Step-by-step explanation:

The radius is given by  r = a (1−cosθ).  

In the Cartesian coordinate system,  x=rcosθ  and  y=rsinθ.  

x=a(1−cosθ)cosθ=a(cosθ−cos2θ),  and,

y=a(1−cosθ)sinθ=a(sinθ−cosθsinθ)=a(sinθ−sin2θ2)  

dxdθ=a(−sinθ+2cosθsinθ)=−a(sinθ−sin2θ),  and,

dydθ=a(cosθ−cos2θ).  

 The slope of the tangent to the curve is,

d y dx=cosθ−cos2θsinθ−sin2θ=m1.  

The slope of the radius vector is  m2=tanθ=sinθcosθ.