Parametric stuff

Question 1

sin²θ from double angle formula

Answer 1

• start from cos2θ = 1-2sin²θ
• sin²θ = 1-cos2θ / 2

Question 2

cos²θ from double angle formula

Answer 2

• start from cos2θ = 2cos²θ - 1
• cos² = 1+cos2θ / 2

Question 3

Volume of Revolution – Parametric Equations

Answer 3

Let:
x = x(t)
y = y(t)
where t ∈ [a, b]

About the x-axis:
V = π ∫ from a to b of [y(t)]² * (dx/dt) dt

About the y-axis:
V = π ∫ from a to b of [x(t)]² * (dy/dt) dt

Question 4

vilume of revolution about x and y axis

Answer 4

Volume of Revolution – About the x-axis
If y = f(x), and x ∈ [a, b]:
V = π ∫ from a to b of [f(x)]² dx

Volume of Revolution – About the y-axis
If x = f(y), and y ∈ [c, d]:
V = π ∫ from c to d of [f(y)]² dy