Question

Soalnya y=4(1-cosθ ) dan x = 4(θ -sinθ )
tentukan dy/dx

Answer 1

Y = 4 - 4cos θ
dy/dθ = 4.sin θ

x = 4θ - 4.sin θ
dx/dθ = 4 - 4cos θ
dθ/dx = 1/(4 - 4cos θ)

dy/dx = (dy/dθ). (dθ/dx)
          = (4.sin θ)/(4 - 4.cos θ)
          = (sin θ)/(1 - cos θ)
          = (2.sin (θ/2).cos (θ/2)/(2.sin² (θ/2))
          = (cos (θ/2))/(sin (θ/2))
          = cotan (θ/2)