Get Expert Graphing Calculator Help for Polar Mode Equations

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SUMMARY

The discussion focuses on graphing the polar equation r² = sin(θ) using TI-83 or TI-84 graphing calculators. Users confirm the necessity of switching to Polar Graphing Calculator (GC) mode instead of Rectangular GC mode. The primary challenge arises from the calculator's limitation to graph only positive values of r, which restricts the representation of the lemniscate to half of its form. To fully graph the lemniscate, users suggest employing both r = √(sin(θ)) and r = -√(sin(θ)) simultaneously, particularly when θ is between π and 2π.

PREREQUISITES
  • Understanding of polar coordinates and equations
  • Familiarity with the TI-83 or TI-84 graphing calculators
  • Knowledge of the properties of the sine function
  • Basic graphing techniques for polar curves
NEXT STEPS
  • Research how to graph polar equations on TI-83 and TI-84 calculators
  • Learn about the properties and characteristics of lemniscates
  • Explore the implications of negative values in polar coordinates
  • Investigate advanced graphing techniques for polar equations
USEFUL FOR

Students, educators, and math enthusiasts interested in graphing polar equations, particularly those using TI-83 or TI-84 calculators and exploring lemniscates.

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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.
The calculator can only graph r !
 
Graph

r= \sqrt{sin \theta }}

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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