covert the rectangular equation to polar form x2+(y+2)2=4
To convert the given rectangular equation to polar form, we will use the following formulas:
x = r * cos(θ)
y = r * sin(θ)
First, let's expand the equation:
x^2 + (y + 2)^2 = 4
Now, replace x and y with their respective polar forms:
(r * cos(θ))^2 + (r * sin(θ) + 2)^2 = 4
Next, simplify the equation:
r^2 * cos^2(θ) + (r * sin(θ) + 2)^2 = 4
Expand and rearrange the equation further:
r^2 * cos^2(θ) + r^2 * sin^2(θ) + 4 * r * sin(θ) + 4 = 4
Combine the terms:
r^2 * (cos^2(θ) + sin^2(θ)) + 4 * r * sin(θ) = 0
Using the trigonometric identity cos^2(θ) + sin^2(θ) = 1, we have:
r^2 + 4 * r * sin(θ) = 0
Finally, we can express this equation in polar form:
r^2 = -4 * r * sin(θ)
This is the polar form of the given equation.