Get Expert Graphing Calculator Help for Polar Mode Equations

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Homework Help Overview

The discussion revolves around graphing the polar equation r² = sin(θ) using a graphing calculator, specifically addressing the challenges associated with representing polar curves and the limitations of the calculator's functionality.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants explore the necessity of using polar graphing mode versus rectangular mode on calculators. There are attempts to clarify how to handle the equation r² = sin(θ) and the implications of graphing only positive values of r. Questions arise regarding how to represent the entire lemniscate given the restrictions of the calculator.

Discussion Status

The discussion is ongoing, with participants providing insights into the limitations of graphing polar equations and exploring alternative methods to represent the lemniscate. There is recognition of the need to consider negative values of r for certain angles, but no consensus has been reached on a definitive solution.

Contextual Notes

Participants note that the graphing calculator may only graph half of the lemniscate due to the nature of the sine function and the restrictions on r values. There is also mention of the challenge in using a single equation to graph the entire shape.

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I am trying to graph: r²= sinθ in Polar mode.
 
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Did you change your calculator to use Polar GC and not Rect GC (assuming you're using a TI-83 or 84).
 
DMOC said:
Did you change your calculator to use Polar GC and not Rect GC (assuming you're using a TI-83 or 84).

Yes, I did. I know how to graph polar curves, but the issue I am having is with r square. r²
The calculator can only graph r !
 
Graph

[tex]r= \sqrt{sin \theta }}[/tex]

instead. r is always positive anyway so you shouldn't miss anything
 
it only graphs half the lemniscate on 0, 2pi

the only way I could find to draw it is using r= square root theta and - square root theta simultaneousely.
 
It should only graph half. If theta is between pi and 2pi, sin(theta) is negative and no value of r will square to a negative number.

EDIT: Unless you allow negative r for a value of theta between pi and 2pi. In which case there's probably no way to graph this on your graphing calculator with a single equation
 
Office_Shredder said:
It should only graph half. If theta is between pi and 2pi, sin(theta) is negative and no value of r will square to a negative number.

EDIT: Unless you allow negative r for a value of theta between pi and 2pi. In which case there's probably no way to graph this on your graphing calculator with a single equation

yeah, I missed that.

But how can we draw a lemniscate then?
 

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