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Classical Curves

Classical Curves. http://www.math.rutgers.edu/~greenfie/mill_courses/math152/diary3.html. r= a sin n θ r= a cos n θ. ROSE CURVES. SINE: starts Quadrant I. COSINE: starts x axis. CARDIOD. r= a + a sin n θ r= a + a cos n θ. Sine (x axis) Cosine (y axis).

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Classical Curves

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  1. Classical Curves

  2. http://www.math.rutgers.edu/~greenfie/mill_courses/math152/diary3.htmlhttp://www.math.rutgers.edu/~greenfie/mill_courses/math152/diary3.html

  3. r= a sin nθ r= a cos nθ ROSE CURVES SINE: starts Quadrant I COSINE: starts x axis

  4. CARDIOD r= a + a sin nθ r= a + a cos nθ Sine (x axis) Cosine (y axis) a + a (distance point to point) ±a (intercepts)

  5. LIMACON r= a + b sin nθ r= a + b cos nθ a + b (distance shape) b – a (distance loop) ± a intercepts a < b b < a a > 2b loop dimple convex (no shape) Cosine (x axis) Sine (y axis)

  6. LEMNISCATE r2= a sin 2θ r2= a cos 2θ Cosine (x axis) Sine (diagonal)

  7. SPIRAL OF ARCHIMEDES r = aθ More spiral (coefficient decimal/small) Less spiral (coefficient larger)

  8. RECTANGULAR TO POLAR R (x, y) P (r, θ) R= (x2 + y2) θ = Arctan (y/x) IF X IS (+) θ = Arctan (y/x) + πIF X IS (-)

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

  10. eo95@ymail.com azzedinr@aol.com turnerkayla23@gmail.com

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