Conversion from
Sexagesimal to Circular System

Worked-out problems on the conversion from sexagesimal to circular system:

1. Express 40° 16’ 24” is radian.

Solution:

40° 16’ 24”

= 40° + 16’ + 24”

We know 1° = 60”

= 40° + 16’ + (24/60)’

= 40° + (16 + 2/5)’

= 40° + (82/5)’

We know 1° = 60’

= 40° + (82/5 × 60)°

= (40 + 41/150)°

= (6041/150)°

We know 180° = πc

Therefore, 6041°/150 = (πc/180) × (6041/150) = 6041/27000 πc

Therefore, 40° 16’ 24” = 6041/27000 πc


2. Show that 1° < 1c

Solution:

We know 180° = πc

or, 1° = (π/180)c

or, 1° = (22/7 × 180) c < 1c

Therefore, 1° < 1c

3. Two angles of a triangle are 75° and 45°. Find the value of the third angle in circular measure.

In ∆ABC, ∠ABC = 75° and ∠ACB = 45°; ∠BAC = ?

You know that the sum of the three angles of a triangle is 180°

Therefore, ∠BAC = 180° - (75° + 45°)

= 180° - 120°

= 60°

Again, we know: 180° = π

Therefore, 60° = 60 π/180 = π/3

In ΔABC, ∠BAC = π/3


4. A rotating ray revolves in the anticlockwise direction and makes two complete revolutions from its initial position and moves further to trace an angle of 30°. What are the sexagesimal and circular measures of the angle with reference to trigonometrical measure?

As the rotating ray does in the anti-clockwise direction, the angle formed is positive. We know, in one complete revolution the rotating ray traces an angle of 360°. So in two complete revolutions it makes an angle of 360° × 2 i.e. 720°. It has moved further to trace an angle of 30°. So the magnitude of the angle formed is (720° + 30°) i.e. 750°

Now, 180° = π

Therefore, 750° = 750 π/180 = 25 π/6


5. The ratio of the angles subtended at the centre by two unequal arcs of a circle is 5 : 3. If the magnitude of the second angle is 45°, find the sexagesimal and circular measures of the first angle.

Let the measure of the first angle be θ°

Then, according to the given condition, θ°/45° = 5/3

Therefore, θ° = 5/3 × 45° = 75°

Again we know, 180° = π

Therefore, 75° = 75 π/180 = 5 π/12

Therefore, the sexagesimal measure of the first angle is 75° and circular measure is 5 π/12.


6. ABC is an equilateral triangle in which AD is the line segment that joins the vertex A to the mid point of the side BC. What is the circular measure of ∠BAD?

Solution:

As ∆ABC is equilateral

Therefore, ∠BAC = 60°

We also know that the median of an equilateral triangle bisects the corresponding vertiealange. Therefore, ∠BAD = 30°

Therefore, the circular measure of ∠BAD = 30 π/180 = π/6

The above solved problems help us to learn in trigonometry, about the conversion from sexagesimal to circular system.

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 Conversion from Sexagesimal to 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. Fraction as a Part of Collection | Pictures of Fraction | Fractional

    Feb 24, 24 04:33 PM

    Pictures of Fraction
    How to find fraction as a part of collection? Let there be 14 rectangles forming a box or rectangle. Thus, it can be said that there is a collection of 14 rectangles, 2 rectangles in each row. If it i…

    Read More

  2. Fraction of a Whole Numbers | Fractional Number |Examples with Picture

    Feb 24, 24 04:11 PM

    A Collection of Apples
    Fraction of a whole numbers are explained here with 4 following examples. There are three shapes: (a) circle-shape (b) rectangle-shape and (c) square-shape. Each one is divided into 4 equal parts. One…

    Read More

  3. Identification of the Parts of a Fraction | Fractional Numbers | Parts

    Feb 24, 24 04:10 PM

    Fractional Parts
    We will discuss here about the identification of the parts of a fraction. We know fraction means part of something. Fraction tells us, into how many parts a whole has been

    Read More

  4. Numerator and Denominator of a Fraction | Numerator of the Fraction

    Feb 24, 24 04:09 PM

    What are the numerator and denominator of a fraction? We have already learnt that a fraction is written with two numbers arranged one over the other and separated by a line.

    Read More

  5. Roman Numerals | System of Numbers | Symbol of Roman Numerals |Numbers

    Feb 24, 24 10:59 AM

    List of Roman Numerals Chart
    How to read and write roman numerals? Hundreds of year ago, the Romans had a system of numbers which had only seven symbols. Each symbol had a different value and there was no symbol for 0. The symbol…

    Read More