Arc LENGTH
L=2(pi)(r)(focus angle/360)
Arc length is the distance along the curved path of an arc. It is the length of a section of a curve between two points on the curve. In mathematics, arc length is a key concept when it comes to understanding and solving problems related to trigonometry, calculus, geometry, and many other areas of mathematics.
To find the arc length of an arc, there are different formulas that can be used depending on the type of curve involved. For instance, one formula that can be used to find the arc length of a circle is:
L = rθ
Where L is the length of the arc, r is the radius of the circle, and θ is the angle that the arc spans. To determine the length of an arc of a circle, we multiply the radius of the circle by the angle of the arc in radians. You can also use degrees instead of radians, but you will need to convert them into radians first.
Another common formula used to find the arc length of a curve is the integral formula. The integral formula is used for finding the arc length of any curve defined by a function. The formula is:
L = ∫baf(x)√(1+[f'(x)]²)dx
Where L is the length of the arc, a and b are the endpoints of the arc, f(x) is the function that defines the curve, and f'(x) is the derivative of the function.
In conclusion, arc length is an essential concept in mathematics that learners should understand. By grasping this concept, you can easily find the length of an arc in any curve or circle using formulas such as the integral formula or circle formula.
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