Circular System

The unit of circular system is based on the constant relation that exists between the circumference of a circle and the radius of that circle.

Circular System

Let us take three concentric circles. From the smallest circle let us cut off an arc AD equal in length to the radius of the circle. O, A and O, D are joined. Then ∠AOD will be an angle at the centre subtended by the arc equal in length to the radius of the circle.

OA and OD are produced to meet other two circles at B, C and E, F respectively. On measurement we will find that BE and CF are equal in length to the radii of the corresponding circles.

So ∠BOE and ∠COF are angles at the centre subtended by arcs equal in length to the respective radii.

Hence we may conclude that an arc of any circle equal in length to the radius of the circle subtends at its centre an angle of constant magnitude. 

One Radia

This angle is taken as the unit of measurement of angles in the circular system.

This is called one radian and written as 1c.

See the magnitude of an angle of one radian in the figure.


Worked-out Examples on Circular System:

In a triangle the angles are in the ratio 2 : 5 : 3, what is the value of the least angle in radian?

Solution:

Let the angles be 2x, 5x and 3x radians.

Therefore, 2x + 5x + 3x = π

or, x = π/10

The least angle in radian is 2x = 2 · π/10 = π/5

Basic Trigonometry 

Trigonometry

Measurement of Trigonometric Angles

Circular System

Radian is a Constant Angle

Relation between Sexagesimal and Circular

Conversion from Sexagesimal to Circular System

Conversion from Circular to Sexagesimal System






9th Grade Math

From Circular System to HOME PAGE


New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.



Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



Share this page: What’s this?

Recent Articles

  1. Multiplication of a Number by a 3-Digit Number |3-Digit Multiplication

    Mar 28, 24 03:48 PM

    Multiplying by 3-Digit Number
    In multiplication of a number by a 3-digit number are explained here step by step. Consider the following examples on multiplication of a number by a 3-digit number: 1. Find the product of 36 × 137

    Read More

  2. Multiply a Number by a 2-Digit Number | Multiplying 2-Digit by 2-Digit

    Mar 27, 24 05:21 PM

    Multiply 2-Digit Numbers by a 2-Digit Numbers
    How to multiply a number by a 2-digit number? We shall revise here to multiply 2-digit and 3-digit numbers by a 2-digit number (multiplier) as well as learn another procedure for the multiplication of…

    Read More

  3. Multiplication by 1-digit Number | Multiplying 1-Digit by 4-Digit

    Mar 26, 24 04:14 PM

    Multiplication by 1-digit Number
    How to Multiply by a 1-Digit Number We will learn how to multiply any number by a one-digit number. Multiply 2154 and 4. Solution: Step I: Arrange the numbers vertically. Step II: First multiply the d…

    Read More

  4. Multiplying 3-Digit Number by 1-Digit Number | Three-Digit Multiplicat

    Mar 25, 24 05:36 PM

    Multiplying 3-Digit Number by 1-Digit Number
    Here we will learn multiplying 3-digit number by 1-digit number. In two different ways we will learn to multiply a two-digit number by a one-digit number. 1. Multiply 201 by 3 Step I: Arrange the numb…

    Read More

  5. Multiplying 2-Digit Number by 1-Digit Number | Multiply Two-Digit Numb

    Mar 25, 24 04:18 PM

    Multiplying 2-Digit Number by 1-Digit Number
    Here we will learn multiplying 2-digit number by 1-digit number. In two different ways we will learn to multiply a two-digit number by a one-digit number. Examples of multiplying 2-digit number by

    Read More