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Relation between radian and degrees

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Relation between radian and degrees

  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 βˆ π΄π‘‚π΅ will be equal to 1 radian. (i.e., βˆ π΄π‘‚π΅ = 1 𝑐 )
  3. 3. www.harekrishnahub.com We have, length of the semi-circular arc = 𝝅𝒓 and the length of the arc 𝑨𝑩 = 𝒓 βˆ π‘¨π‘Άπ‘© = 𝟏 𝒄 and βˆ π‘·π‘Άπ‘Έ = πŸπŸ–πŸŽΒ° = 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 βˆ π‘¨π‘Άπ‘© = 𝒂𝒓𝒄 𝑷𝑸 βˆ π‘·π‘Άπ‘Έ 𝒓 𝟏 𝒄 = 𝝅𝒓 𝒙 𝒄 𝒙 𝒄 𝟏 𝒄 = 𝝅𝒓 𝒓 = 𝝅 ∴ 𝒙 = 𝝅 𝒄 but 𝒙 = πŸπŸ–πŸŽΒ° ∴ πŸπŸ–πŸŽΒ° = 𝝅 𝒄
  4. 4. www.harekrishnahub.com In practise, the subscript for radian is usually omitted. It is therefore, understood that ∴ 𝝅 𝒄 = πŸπŸ–πŸŽΒ° 𝝅 = 𝟐𝟐 πŸ• = πŸ‘. πŸπŸ’πŸ ∴ πŸ‘. πŸπŸ’πŸ 𝒄 = πŸπŸ–πŸŽΒ° 𝝅 ⟹ πŸπŸ–πŸŽΒ°
  5. 5. www.harekrishnahub.com some examples: Degrees Radians 360 πŸπ›‘ 270 πŸ‘π›‘ 𝟐 180 𝛑 90 𝛑 𝟐 60 𝛑 πŸ‘ 45 𝛑 πŸ’ 30 𝛑 πŸ”

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