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(III) The Circular system (or the Circular measure) : This system is commonly used in all the higher branches of mathematics.

The only unit of this system is a radian (c)

* A radian (rad) is defined as the measure of an angle     subtended by an arc of a     circle equal to the radius of the     circle. The circumference of a circle = 2 pr and subtends an     angle of 3600Then 2p (rad) = 3600

 

Theorem :

A radian is independent of the radius of the measuring circle.


EXAMPLE 2

Convert 60 13' 18 to degrees in decimal notation.


Solution :

We know 1' = (1/60)0 and 1" = (1 / 60)'


EXAMPLE 3

Convert 87.41290 to degrees, minutes and seconds.


Solution :

Firstly 0.41290 = 0.4129 (60') = 24.774'

Also, 0.774' = 0.774 (60") = 46.44"

Thus 87.41290 = 870 24' 46.44"

 

EXAMPLE 4

Convert 1 rad into degrees, minutes and seconds.


Solution :

EXAMPLE 5

Convert 1 degrees to radians


Solution :

 

[next page]

 

Index

1.1 Angles (Radians & Degrees)
1.2 Arc Length & Area of the circle
Supplementary Problems

Chapter 2





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