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




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.



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.




Share this page: What’s this?

Recent Articles

  1. Construction of Bar Graphs | Examples on Construction of Column Graph

    Jul 30, 25 03:20 PM

    What is Bar Graph?
    Now we will discuss about the construction of bar graphs or column graph. In brief let us recall about, what is bar graph? Bar graph is the simplest way to represent a data. In consists of rectangular…

    Read More

  2. Successor and Predecessor | Successor of a Whole Number | Predecessor

    Jul 29, 25 12:59 AM

    Successor and Predecessor
    The number that comes just before a number is called the predecessor. So, the predecessor of a given number is 1 less than the given number. Successor of a given number is 1 more than the given number…

    Read More

  3. Worksheet on Area, Perimeter and Volume | Square, Rectangle, Cube,Cubo

    Jul 28, 25 01:52 PM

    Volume of a Cuboids
    In this worksheet on area perimeter and volume you will get different types of questions on find the perimeter of a rectangle, find the perimeter of a square, find the area of a rectangle, find the ar…

    Read More

  4. Worksheet on Volume of a Cube and Cuboid |The Volume of a RectangleBox

    Jul 25, 25 03:15 AM

    Volume of a Cube and Cuboid
    We will practice the questions given in the worksheet on volume of a cube and cuboid. We know the volume of an object is the amount of space occupied by the object.1. Fill in the blanks:

    Read More

  5. Volume of a Cuboid | Volume of Cuboid Formula | How to Find the Volume

    Jul 24, 25 03:46 PM

    Volume of Cuboid
    Cuboid is a solid box whose every surface is a rectangle of same area or different areas. A cuboid will have a length, breadth and height. Hence we can conclude that volume is 3 dimensional. To measur…

    Read More