How to graph r^2 = sin \theta in polar coordinates using TI-89

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To graph the equation r^2 = sin(θ) in polar coordinates using a TI-89, it is suggested to plot r = √(sin(θ)) for θ in the range [0, π]. The negative root, r = -√(sin(θ)), is unnecessary since r must be non-negative in polar coordinates. This equation represents a Lemniscate, a figure-eight shaped curve. Users unfamiliar with the TI-89 may need to familiarize themselves with its graphing functions. Understanding the nature of polar coordinates is essential for accurate graphing.
Bachelier
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In polar equations, how can I graph r^2= sin \theta on TI-89?

The r is squared. I tried to graph r = sqrt(sin \theta ) and r = -sqrt(sin \theta ) separately on [0, \pi ], however I am not sure this is the correct answer?

thx
 
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Hi Bachelier! :smile:

(have a theta: θ and a pi: π and a square-root: √ and try using the X2 tag just above the Reply box :wink:)

(I don't know anything about the TI-89, but … )

If this r and θ are the usual polar coordinates, then r can't be negative, and so you don't need r = -√(sinθ). :wink:
 
the formula in polar coordinates is that of a Lemniscate:

r squared equals sin (theta)

I am used to graphing R, not R squared.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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