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

Answer: x^2 + y^2 - 10y = 0

Step-by-step explanation:

Cartesian coordinates, also called the Rectangular coordinates, isdefined in terms of x and y. So, for the problem θ has to be eliminated or converted using basic foundations that are described by the unit circle and the right triangle trigonometry.

r = 10sin (θ)

Remember that:

x = r * cos (θ)

y = r * sin (θ)

r^2 = x^2 + y^2

Multiply both sides of the equation by r. This will give:

r * r = 10r * sin (θ)

r^2 = 10r * sin (θ)

x^2 + y^2 = 10r * sin (θ)

Because y = r * sin (θ), we can make a substitution. This will be:

x^2 + y^2 = 10y

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

The above equation is the Rectangular coordinate equivalent to the given equation.