Describe the differences between the rectangular coordinate system and the polar coordinate system.

Step by Step Solution: Step 1. The rectangular coordinate system represents points in a 2-dimensional plane using a pair of coordinates (x,y), where x is the horizontal distance and y is the vertical distance from the origin. Step 2. The polar coordinate system represents points in a 2-dimensional plane using a pair of coordinates (r,θ), where r is the distance from the origin to the point and θ is the angle formed by the positive x-axis and the line connecting the origin to the point. Step 3. The rectangular coordinate system is more commonly used, especially in basic algebra and geometry, while the polar coordinate system is commonly used in advanced mathematics and physics, such as calculus and electromagnetism. Step 4. Converting between rectangular and polar coordinates involves using the equations x = r*cos(θ) and y = r*sin(θ) to convert from polar to rectangular coordinates, and using the equations r = sqrt(x^2 + y^2) and θ = atan(y/x) to convert from rectangular to polar coordinates. Step 5. The rectangular coordinate system has rectangular symmetry and polar symmetry while the polar coordinate system has rotational symmetry. Step 6. The rectangular coordinate system is limited to working with rectangular shapes while the polar coordinate system is more adept at working with radial shapes.