Question

Find dy/dx , when -
x=a(1-cos∅) and y=a(∅+sin∅)
[Derivatives of Parametric equations]
ΔΔΔΔΔΔΔΔΔΔΔΔΔΔΔΔΔΔΔ

Answer 1

Assuming you know how to do simple derivatives for functions like x, and sinx, I've skipped the actual derivatives part. But the division of the derivatives is the main concept in parametric derivatives.

Answer 2

We know that

sin2∅ = 2sin∅ cos∅

Replacing ∅ with ∅/2

sin∅= 2sin∅/2 cos∅/2

Also, cos2∅=1-2sin^2∅

2sin^∅=1 - cos2∅

Replacing ∅ with ∅/2

2sin^2 ∅/2=1-cos∅