Chord length = 2Sina, the origin of this formula is based on the nature of circle and the definition of trigonometric function. In a circle, the length of a chord is related to the central angle. The greater the central angle, the longer the chord; The smaller the central angle, the shorter the chord. At the same time, the length of the chord is also related to the radius of the circle. The larger the radius, the shorter the chord; The smaller the radius, the longer the chord.
Therefore, we can express the length of a chord as a function of the radius and central angle of a circle. According to the definition of trigonometric function, sina is the sine of the central angle a, so the chord length can be expressed as 2Rsina. This formula can be used to calculate the length of any chord on a circle and solve many geometric problems.
To better understand this formula, we can consider a concrete example. Suppose there is a circle with a radius of 3 cm and a central angle of 60 degrees. The radius of the circle is 3 cm and the central angle is 60 degrees. According to the formula of circular chord length, chord length = 2r× Sina = 6s in (0.33333333 pi) cm. Therefore, the chord length of a circle is 6s inches (0.3333333 skin) cm.
Function of arc length formula of circle;
1, calculate arc length: the arc length formula can be used to calculate the length of any arc on a circle. In geometry, graphics, physics and other disciplines, the arc length formula is widely used to calculate the relative length of a circle or arc. The arc length formula can accurately calculate the length of the arc by inputting the radius of the circle and the central angle of the arc, which provides an important numerical basis for studying the properties and characteristics of the circle or arc.
2. Derive the properties of the circle: Through the arc length formula, we can further deduce and prove the properties and theorems related to the circle. For example, using the formula of arc length and calculus, we can find out the circumference of a circle, and then study the geometric characteristics of the circle such as radius and diameter. The formula of arc length plays a key role in deducing the properties and theorems of circles and has made important contributions to the development of mathematics.
3. Solving practical problems: Arc length formula is also widely used in solving practical problems. For example, in engineering, the arc length formula can be used to calculate and design the length of curves, pipes, etc. In physics, the arc length formula can be used to study the trajectory and velocity of objects. In geography, the arc length formula can be used to calculate the distance between two points on the earth. The arc length formula has a wide range of applications, involving the solution of problems in various fields.