Find an equation equivalent to r = 10 sin theta in rectangular coordinates.

r = 10sinθ

Is

x² + (y - 5) ² = 25

in rectangular coordinates.

Step-by-step explanation:

To convert r = 10sinθ to rectangular coordinates,

First, note the following equivalents

r² = x² + y²

x = rcosθ

y = rsinθ

=> sinθ = y/r

Now, r = 10sinθ

Implies

r = 10 * y/r

Multiply both sides by r

r² = 10y

Since r² = x² + y², we have

x² + y² = 10y

Or

x² + y² - 10y = 0

Completing the square for y² - 10y, we have

x² + [y² - 2 (5) y + 5² - 5²] = 0

x² + (y - 5) ² - 25 = 0

x² + (y - 5) ² = 25

Centered at (0, 5) with radius 5

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