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
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