The document discusses the relationship between radians and degrees. It explains that 1 radian is defined as the angle subtended by an arc of a circle that is equal in length to the circle's radius. This means that for a full circle, the angle is 2π radians or 360 degrees. It also provides some examples of common angle measurements in both radians and degrees.

1. Relation between radian and degrees
by
SBR
www.harekrishnahub.com

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• Consider a circle with centre O and radius
r units.
• Let PQ be the diameter of the circle.
• Let A and B be any points on the circle,
such that the length of the arc AB is equal
to the radius r of the circle.
• Then the angle ∠𝐴𝑂𝐵 will be equal to 1
radian. (i.e., ∠𝐴𝑂𝐵 = 1 𝑐
)

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We have, length of the semi-circular arc = 𝝅𝒓 and the length of the arc 𝑨𝑩 =
𝒓
∠𝑨𝑶𝑩 = 𝟏 𝒄
and ∠𝑷𝑶𝑸 = 𝟏𝟖𝟎° = 𝒙 𝒄
(say)
We know that in a circle, the arc lengths are proportional to the angles
subtended by them at the centre. Therefore,
𝒂𝒓𝒄 𝑨𝑩
∠𝑨𝑶𝑩
=
𝒂𝒓𝒄 𝑷𝑸
∠𝑷𝑶𝑸
𝒓
𝟏 𝒄 =
𝝅𝒓
𝒙 𝒄
𝒙 𝒄
𝟏 𝒄
=
𝝅𝒓
𝒓
= 𝝅
∴ 𝒙 = 𝝅 𝒄
but 𝒙 = 𝟏𝟖𝟎°
∴ 𝟏𝟖𝟎° = 𝝅 𝒄

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In practise, the subscript for radian is usually omitted.
It is therefore, understood that
∴ 𝝅 𝒄 = 𝟏𝟖𝟎°
𝝅 =
𝟐𝟐
𝟕
= 𝟑. 𝟏𝟒𝟐
∴ 𝟑. 𝟏𝟒𝟐 𝒄 = 𝟏𝟖𝟎°
𝝅 ⟹ 𝟏𝟖𝟎°

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some examples:
Degrees Radians
360 𝟐𝛑
270
𝟑𝛑
𝟐
180 𝛑
90
𝛑
𝟐
60
𝛑
𝟑
45
𝛑
𝟒
30
𝛑
𝟔