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

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