Classical Curves

fie/mill_courses/math152/diary3.htm l

ROSE CURVES r= a sin n θ r= a cos n θ SINE: starts Quadrant I COSINE: starts x axis

CARDIOD r= a + a sin n θ r= a + a cos n θ a + a (distance point to point) ±a (intercepts) Sine (x axis) Cosine (y axis)

LIMACON a + b (distance shape) b – a (distance loop) ± a intercepts a 2b loopdimpleconvex (no shape) r= a + b sin n θ r= a + b cos n θ Cosine (x axis) Sine (y axis)

LEMNISCATE r 2 = a sin 2 θ r 2 = a cos 2 θ Cosine (x axis) Sine (diagonal)

SPIRAL OF ARCHIMEDES r = a θ More spiral (coefficient decimal/small) Less spiral (coefficient larger)

RECTANGULAR TO POLAR R (x, y) P (r, θ) R= (x 2 + y 2 ) θ = Arctan (y/x) IF X IS (+) θ = Arctan (y/x) + π IF X IS (-)

POLAR TO RECTANGULAR P (r, θ) R (x, y) X = r cos θY = r sin θ