shamieh said:This may seem like a dumb question, but is finding the "arc length" of a curve and finding the "length" of a curve the same thing? Just worded differently?
Arc length is the measure of the distance along the curved line of an arc. It is typically denoted by the symbol "s" and is measured in units of length, such as meters or feet.
To find the arc length, you can use the formula s = rθ, where s is the arc length, r is the radius of the arc, and θ is the central angle of the arc measured in radians. Alternatively, you can use the formula s = 2πr(n/360), where n is the central angle measured in degrees.
Arc length refers to the distance along the curved line of an arc, while length refers to the distance between two points in a straight line. Arc length is typically longer than the length of the chord connecting the two endpoints of the arc.
No, the arc length of an arc cannot be longer than the circumference of a circle. The circumference is the longest possible distance that can be measured on a circle, and the arc length is always a portion of the circumference.
Arc length is used in various fields, including mathematics, physics, engineering, and architecture. It is commonly used in calculating the distance traveled by a moving object along a curved path, determining the size of a sector of a circle, and designing curved structures such as bridges and arches.