Chord modulus

Chord Modulus

The chord modulus is a mathematical concept used in the field of geometry and trigonometry. It is defined as the length of a chord that subtends a given angle at the center of a circle. The chord modulus is denoted by the symbol "c".

Definition

Let's consider a circle with radius "r" and center "O". Suppose we have a chord AB that subtends an angle θ at the center of the circle. The chord modulus, denoted as "c", is the length of the chord AB.

Calculation

To calculate the chord modulus, we can use the following formula:

c = 2 * r * sin(θ/2)

Here, "r" represents the radius of the circle, and θ is the angle subtended by the chord at the center of the circle.

Properties

1. The chord modulus is always positive. 2. The chord modulus is directly proportional to the radius of the circle. 3. The chord modulus is also directly proportional to the sine of half the angle subtended by the chord.

Applications

The chord modulus finds applications in various fields, including:

1. Geometry: The chord modulus is used to calculate the length of a chord in a circle, which is essential in solving problems related to circles and their properties. 2. Trigonometry: The chord modulus is used in trigonometric calculations involving circles, such as finding the length of a chord given the radius and the angle subtended by the chord. 3. Engineering: The chord modulus is used in engineering applications, such as designing circular structures or calculating the length of cables or ropes required to span a given distance.

See Also

• Circle (geometry)
• Trigonometry
• Radius
• Sine function

References

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