Polar equations are mathematical expressions that describe a curve or shape in a polar coordinate system. They involve a variable radius and angle, rather than x and y coordinates.
To find the shared area of 2 polar equations, you need to graph both equations on the same polar coordinate plane. Then, find the points where the curves intersect and use the formula for finding the area between 2 polar curves, which is A = 1/2∫[r1^2-r2^2]dθ, where r1 and r2 are the radii of the curves at each point of intersection.
Rectangular equations use x and y coordinates to graph a curve or shape, while polar equations use a variable radius and angle. Rectangular equations are more commonly used in traditional algebraic graphing, while polar equations are often used in physics and engineering to describe circular or rotational motion.
Yes, polar equations can be converted to rectangular equations and vice versa. This can be done by using the formulas x = rcosθ and y = rsinθ to convert from polar to rectangular, and x^2 + y^2 = r^2 to convert from rectangular to polar.
Polar equations have many real-world applications, such as in physics for describing rotational motion, in engineering for designing circular structures, and in astronomy for mapping the positions of celestial objects. They are also used in computer graphics to create 3D shapes and animations.