Question

Rewrite r = 3.5 sin θ in rectangular form.
(1 point)
Responses

x squared plus y squared minus 12.25 x equals 0
Image with alt text: x squared plus y squared minus 12.25 x equals 0

x squared plus y squared minus 3.5 y equals 0
Image with alt text: x squared plus y squared minus 3.5 y equals 0

x squared plus y squared plus 1.9 y equals 0
Image with alt text: x squared plus y squared plus 1.9 y equals 0

x squared minus y squared plus 07 y equals 0
Image with alt text: x squared minus y squared plus 07 y equals 0

Answer 1

To convert the polar equation \( r = 3.5 \sin \theta \) into rectangular form, we can use the relationships between polar and rectangular coordinates:

- \( r^2 = x^2 + y^2 \)
- \( x = r \cos \theta \)
- \( y = r \sin \theta \)

Starting with \( r = 3.5 \sin \theta \):

1. Multiply both sides by \( r \) to eliminate \( r \) on the left:
\[
r^2 = 3.5 r \sin \theta
\]

2. Substitute \( r^2 \) with \( x^2 + y^2 \) and \( r \sin \theta \) with \( y \):
\[
x^2 + y^2 = 3.5 y
\]

3. Rearrange the equation to get it in standard form:
\[
x^2 + y^2 - 3.5 y = 0
\]

So the rectangular form of the equation \( r = 3.5 \sin \theta \) is

\[
\mathbf{x^2 + y^2 - 3.5 y = 0}
\]

Therefore, the correct response is:

**x squared plus y squared minus 3.5 y equals 0**.