Pure: Sine and Cosine Rule

A. Definition and Cartesian Equations of a Circle Definition: A circle is defined as the locus of a point that moves in a plane such that its distance from a fixed point (the center) is always constant (the radius). Explanation: This fundamental definition means that every point on the circumference of a circle is equidistant from its center. Based on this, we can derive different forms of the circle's equation. The simplest is when the center is at the origin, and it becomes more general when the center is at any point (a,b) or when expressed in its expanded general form. Think of it as: Imagine a dog tied to a pole with a leash. The pole is the center, the leash is the radius, and the path the dog can walk, keeping the leash taut, forms a circle. Real-world application: Circles are used in engineering to design wheels, gears, and pipes. In architecture, circular designs are common in domes and arches, providing structural strength and aesthetic appeal. GPS systems use circular principles to determine location based on distances from satellites. B.