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RADIANS

r. r. Ø=1radian. r. RADIANS. Definition An arc of length r subtends an angle of one radian at the centre of a circle of radius r. r. r. Ø=1radian. r. Proof. How do you calculate the length of an arc?. r = ø x 2πr 360º. r = 1 radian x 2πr 360 º. x 360 º.

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RADIANS

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  1. r r Ø=1radian r RADIANS Definition An arc of length r subtends an angle of one radian at the centre of a circle of radius r

  2. r r Ø=1radian r Proof How do you calculate the length of an arc? r =ø x 2πr 360º r = 1 radian x 2πr 360 º x 360 º 360r = 1 radian x 2πr ÷ r 360 º = 1 radian x 2π ÷ 2 180 º = 1 radian x π Or 180 º = π radians ÷ π 180 = 1 radian π so 1 radian is approximately…?

  3. Converting between angles and radians Degrees = radians x 180 π Radians = degrees x π 180 So if ø is measured in radians Then ø radians = ø x π 180

  4. 90º = πradians 2 How many different angles can you write as radians? 180º = π radians

  5. r r Ø=1radian r Arc Length Angle in degrees Arc length = ø x 2πr 360º Arc length = 2πrø 360º Factorise r Arc length = r 2πø 360º Divide by 2 Angle in radians Arc length = r πø 180º Arc length = rø

  6. r r Ø=1radian r Area of Sector Angle in degrees Sector area = ø x πr2 360º Sector area = πr2ø 360º Factorise r2 Sector area = r2 πø 360º Factorise out ½ Angle in radians Sector area = ½r2πø 180º Sector area = ½r2ø

  7. Examples Convert 50° into radians 50° = 50° x π rad 180 50° = 0.87 rad

  8. Examples Convert 2.7 radians into degrees 2.7 rad = 2.7 x 180 degrees π 2.7 rad = 154.7 °

  9. Examples Convert 40° into radians 40° = 40 x π 180 40° = 40π 180 40° = 2π radians 9

  10. Calculate the arc length and sector area 10cm 1.2radians Arc length = rө Arc length = 10 x 1.2 Arc length = 12cm Sector area = ½r2ө Area = ½ x 100 x 1.2 Area = 60cm2

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