Parametric Equations, Polar Coordinates & Vector-Valued Functions Glossary

int speed dt or int sqrt(r^2+r_prime^2) dtheta.

Heart-shaped: r=a(1+/-cos theta).

Rolling circle: x=a(t-sin t),y=a(1-cos t).

r(b)-r(a).

r=a e^(b theta), constant angle with radii.

Figure-eight: r^2=a^2 cos(2theta).

r=a+b cos theta. a=b:cardioid. a<b:loop. a>b:convex.

x=f(t),y=g(t) describing curve via t.

(r,theta): distance and angle from origin.

r=a cos(n theta): petal loops.

|v|=sqrt(x_prime^2+y_prime^2).

r(t)=<x(t),y(t)>: scalar to vector.