Method of Calculating Area and Arc Length of Sine and Cosine Functions in Polar Coordinates

The region area is the measurement of two-dimensional surface bounded by a curve. The region area is determined using an integral, based on the distance between points rotating according to the rotation angle. The arc length is a measure of the distance along the curved line formed by the curve. The arc length is determined using an integral, based on the distance between points rotating according to the rotation angle. The arc length is the length of the curve. The purpose of this study was to find the area and the arc length of a figure formed by a curve using polar coordinates. The results obtained that the region area be formed by a curve is directly proportional to the square of the curve function, while the arc length on the curve is influenced by the square of the curve function and its first derivative. Simulations were performed on sine and cosine functions.