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File: photo_2023-11-20_16-39-13.jpg (168 KB, 1280x1018)
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So I turned it into regular rectangular form equation but the graph isn't coming right. I'll be attaching my conversion, the graph i got and the actual graph.
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File: firefox_pmHflOs8wb.png (53 KB, 1252x637)
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The Graph from the reduction
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File: Acrobat_aa20eG7nUz.png (25 KB, 306x335)
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Actual Graph
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>>1420002
Hard to follow, but I noticed on the first line
> cos 2θ = √((1+cos θ)/2)
which is backwards. The correct formula is
> cos(θ/2) = √((1+cos θ)/2)
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>>1420012
(continued)

So the correct formula is
r = cos(2θ) = 2cos^2(θ) - 1
with x = r cos(θ) we get
r = 2(x/r)^2 - 1
multiplying both sides by r^2:
r^3 = 2x^2 - r^2
r^3 + r^2 = 2x^2
x = √((r^3 + r^2)/2) = r√((1+r^2) / 2)
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File: desmos.png (23 KB, 975x357)
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>>1420014
(continued)

from
x^2 = (r^3 + r^2) / 2
we get
x^2 = ((x^2 + y^2)^(3/2) + (x^2 + y^2)) / 2

I only get half of the expected plot. I think this is because squaring gets rid of some minus signs. I have to think about it.
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File: desmos.png (28 KB, 866x431)
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>>1420016
(continued)

A minus sign gives the other half. I'm not sure how to get them both in Desmos.
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File: desmos.png (27 KB, 800x349)
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(continued)

So the plot from your textbook doesn't restrict r to positive values only. The vertical leaves of the rose correspond to parts where r=cos(2θ) is negative.

So we have
r = ±√(x^2 + y^2)
The minus sign disappears in the term r^2 but not in the term r^3.
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>>1420012
WHAT THE FUCK, I need to sleep. Thank you very much brother.
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>>1420017
There are tabs to write below where you wrote the top equation.
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>>1420002
you know you can plot polar plots in desmos right? just use r and theta
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File: desmos.png (43 KB, 1090x372)
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>>1420030
Didn't know that, but the point is to practice conversion between polar and rectangular coordinates and check his answer.
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>>1420020
How can Root x2 + y2 be negative, sum of two squares will always be positive.
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>>1420262
it wont be
but the solution to a^2 = b is +-sqrt(a) = b
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>>1420263
other way around
+-sqrt(b) = a
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>>1420263
Yep i got it, i am a dumb fuck. In case of variables there's always plus and minus case.
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>>1420005
What book?
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File: stewart-calculus-9ed.png (58 KB, 839x678)
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>>1420270
looks like Stewart Calculus, but OP seems to have a different edition
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>>1420643
OP here,

It's from Pre-Calculus by Stalwart, Chapter - 8



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