Polar and Parametric Equations Formula Sheet, Cheat Sheet of Calculus

Download Polar and Parametric Equations Formula Sheet and more Cheat Sheet Calculus in PDF only on Docsity! Formula Sheet Parametric Equations: x = f(t), y = g(t), α ≤ t ≤ β Slope of a tangent line: dy dx = dy dt dx dt = g′(t) f ′(t) Area: ∫ β α g(t)f ′(t)dt Arclength: ∫ β α √ (f ′(t))2 + (g′(t))2dt Surface area: ∫ β α 2πg(t) √ (f ′(t))2 + (g′(t))2dt Polar Equations: r = f(θ), α ≤ θ ≤ β Polar coordinates to cartesian: x = r cos(θ), y = r sin(θ) Cartesian coordinates to polar: r = √ x2 + y2, θ = arctan (y x ) Slope of a tangent line: dy dx = dy dθ dx dθ = f ′(θ) sin(θ) + f(θ) cos(θ) f ′(θ) cos(θ)− f(θ) sin(θ) Area: ∫ β α 1 2 (f(θ))2dθ Arclength: ∫ β α √ (f ′(θ))2 + (f(θ))2dθ