Find an equation equivalent to r = 10 sin theta in rectangular coordinates. Question Find an equation equivalent to r = 10 sin theta in rectangular coordinates. in progress 0 Math Natalia 10 hours 2021-11-25T12:04:11+00:00 2021-11-25T12:04:11+00:00 2 Answers 0 views 0

## Answers ( )

Answer:i put c

Step-by-step explanation:Answer:

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