Rewrite the following polar equation in rectangular form. r=−10sinθ

The polar equation given is r = -10sinθ.

To convert this to rectangular form, we can use the relationship between polar and rectangular coordinates. In polar coordinates, r is the distance from the origin and θ is the angle from the positive x-axis. In rectangular coordinates, x = rcosθ and y = rsinθ.

Substitute y = rsinθ into the given polar equation:

r = -10sinθ becomes r = -10(y/r)

Multiply both sides by r to get rid of the fraction:

r^2 = -10y

In polar coordinates, r^2 = x^2 + y^2. So we can substitute x^2 + y^2 for r^2:

x^2 + y^2 = -10y

Rearrange the equation to get it in standard form:

x^2 + y^2 + 10y = 0

This is the rectangular form of the given polar equation.