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Radian

The document explains the concept of radians, defining one radian as the angle subtended at the center of a circle when the arc length equals the radius. It provides formulas for converting between degrees and radians, along with examples demonstrating these conversions. The relationships between radians and degrees are also illustrated, showing that 1 radian equals 180/π degrees and 360 degrees equals 2π radians.

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vashnadevi
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37 views2 pages

Radian

The document explains the concept of radians, defining one radian as the angle subtended at the center of a circle when the arc length equals the radius. It provides formulas for converting between degrees and radians, along with examples demonstrating these conversions. The relationships between radians and degrees are also illustrated, showing that 1 radian equals 180/π degrees and 360 degrees equals 2π radians.

Uploaded by

vashnadevi
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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2/4/25, 3:01 PM Radian

 Back

Radian

1.1 Radian

Mind map titled 'Radian' illustrating the formula for converting radians to degrees.

Definition of One Radian

Definition
The angle subtended at the centre of a circle is 1 radian if the length of the arc is equal to the radius of the circle.

Figure

Relationship with Degrees

180∘
1 rad = ​

π
360∘ = 2π rad

© 2025 Pandai.org All Rights Reserved


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2/4/25, 3:01 PM Radian

Conversion Formula

To convert degrees to radians:


π
radians = degrees ×
180∘
​

To convert radians to degrees:


180∘
degrees = radians × ​

Example 1

Question
Convert 120∘ to radians.

Solution
π
radians = 120∘ ×
180∘
​

​ ​

2π
= rad.
3
​

Example 2

Question
π
Convert rad to degrees.
4
​

Solution
∘
π 180
degrees = rad ×
4 π
​ ​

​ ​

= 45∘ .

© 2025 Pandai.org All Rights Reserved


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