<Content edited by mentor>BvU said:Try ##\theta=0##
trew said:
Thread moved for this reason.Ray Vickson said:
A polar curve is a graph that shows the relationship between the distance of a point from the origin and its angle from a reference direction. It is commonly used to represent mathematical equations in polar coordinates.
A regular curve is represented in Cartesian coordinates, where the x and y values are plotted on a rectangular grid. In contrast, a polar curve is represented in polar coordinates, where the distance from the origin and angle from a reference direction are plotted on a polar grid.
The formula for finding the area of a polar curve is A = ∫ 1/2 * r^2 dθ, where r is the distance of a point from the origin and θ is the angle from a reference direction. This integral represents the sum of infinitely small areas under the curve.
Yes, a polar curve can represent a rectangular shape if the equation for the curve follows the form r = a cos(nθ) or r = a sin(nθ), where a is the length of the sides of the rectangle and n is an integer representing the number of sides. This is known as a "cardioid" shape.
Polar curves have many practical applications in fields such as engineering, physics, and astronomy. They can be used to model the motion of planets and satellites, analyze the strength and direction of electric fields, and design efficient structures such as bridges and antennas.
