Sure, to find the equivalent polar form for the given rectangular equation x^2 + y^2 = 64, we first need to know what a polar equation is and how we convert between Cartesian and polar coordinates.
The Cartesian coordinates are given by two values (x, y), whereas in the polar coordinate system, a point is determined by the distance from the origin, which is the radius 'r', and the angle 'θ' measured from the positive x-axis.
The rectangular equation x^2 + y^2 = 64 is the equation of a circle with a center at the origin and a radius which is the square root of 64, which equals to 8.
To convert this to polar coordinates, we remember that in the polar coordinate system, the radius 'r' is equivalent to the distance from the origin to the point on the plane.
In this case, since the circle has a radius of 8, any point on this circle will have a distance of 8 from the origin.
Therefore, in the polar coordinate system, 'r' (which is the distance from the origin to any point on the plane) will be equal to 8.
So, the equivalent polar form of the rectangular equation x^2 + y^2 = 64 is r = 8.