Convert to polar coordinates with r greater than or equzl to 0 and theta between 0 degrees and 360 degrees
Write the equation inpolar coordinates
x squared + y squared = 2
r^2 cos^2 theta + r^2 sin^2 theta = 2
r^2 (cos^theta + sin^2 theta) = r^2 = 2
r = sqrt 2 ; theta = anything
This is a circle with radius sqrt 2.
To convert the equation x^2 + y^2 = 2 to polar coordinates, we can use the following substitutions:
x = r * cos(theta)
y = r * sin(theta)
Substituting these values into the equation, we get:
(r * cos(theta))^2 + (r * sin(theta))^2 = 2
Expanding and simplifying the equation, we have:
r^2 * cos^2(theta) + r^2 * sin^2(theta) = 2
Since cos^2(theta) + sin^2(theta) = 1, we can simplify the equation further:
r^2 * (cos^2(theta) + sin^2(theta)) = 2
r^2 = 2
Therefore, in polar coordinates, the equation x^2 + y^2 = 2 can be written as r^2 = 2.