trapking504 trapking504
  • 21-05-2020
  • Mathematics
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Convert the rectangular equation x ^ 2 + y ^2 = 2 y to polar form

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altavistard
altavistard altavistard
  • 02-03-2022

Answer:

Step-by-step explanation:

The main equivalence between rectangular and polar forms is

x^2 + y^2 = r^2, where r is the radius.  Next, y = r sin Ф.  Thus,

x^2 + y^2 = r^2 becomes r² = 2·r·sin Ф.

The variable r can be factored out partially:  r = 2·sin Ф

This is the polar form of x^2 + y^2 = 2y.

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