Sunday, November 14, 2021

Casio fx-CG 50: Functions as Polar Graphs

Casio fx-CG 50:  Functions as Polar Graphs


Introduction


The function y = f(x) and equations in the form f(x,y) = g(x,y) can be transformed into its polar form by applying the transformations:


x = r cos Θ

y = r sin Θ


It can be a challenge getting the transformed equation in the form r = w(Θ), but it seems to work best where f(x,y) and g(x,y) are polynomials.   


The following are graphs generated with a Casio fx-CG 50:


Function, y(x):   green with connected line

Polar Function, r(Θ):  blue with dots 


Graphs


# 1:

y = x^2, r = sin Θ ÷ (cos Θ)^2 and r = 0





# 2:

y = x^3, r = ±√(sin Θ) ÷ (cos Θ)^(2/3) and r = 0





# 3:

y = 3x - 4, r = 4 ÷ (3 cos Θ - sin Θ)





General:  y = ax + b, r = -b ÷ (a cos Θ - sin Θ)


# 4:

y = 1/3 * (x - 4), r = -4 ÷ (3 sin Θ - cos Θ)





General:  ay = x + b, r = b ÷ (a sin Θ - cos Θ)


# 5:

y = ±√x, r = cos Θ ÷ (sin Θ)^2





# 6:

y = x^2 + x, r = tan Θ ÷ cos Θ - 1 ÷ cos Θ





# 7:

y = 1/x, r = √(1 ÷ (cos Θ sin Θ))





Eddie 


All original content copyright, © 2011-2021.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 


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