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This presentation illustrates the relation between radian and degrees

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1. 1. Relation between radian and degrees by SBR www.harekrishnahub.com
2. 2. www.harekrishnahub.com β’ Consider a circle with centre O and radius r units. β’ Let PQ be the diameter of the circle. β’ 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. β’ Then the angle β π΄ππ΅ will be equal to 1 radian. (i.e., β π΄ππ΅ = 1 π )
3. 3. www.harekrishnahub.com We have, length of the semi-circular arc = ππ and the length of the arc π¨π© = π β π¨πΆπ© = π π and β π·πΆπΈ = πππΒ° = π π (say) We know that in a circle, the arc lengths are proportional to the angles subtended by them at the centre. Therefore, πππ π¨π© β π¨πΆπ© = πππ π·πΈ β π·πΆπΈ π π π = ππ π π π π π π = ππ π = π β΄ π = π π but π = πππΒ° β΄ πππΒ° = π π
4. 4. www.harekrishnahub.com In practise, the subscript for radian is usually omitted. It is therefore, understood that β΄ π π = πππΒ° π = ππ π = π. πππ β΄ π. πππ π = πππΒ° π βΉ πππΒ°
5. 5. www.harekrishnahub.com some examples: Degrees Radians 360 ππ 270 ππ π 180 π 90 π π 60 π π 45 π π 30 π π