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  1. Glossary
  2. /Mathematics
  3. /Radian

What is Radian?

In short

A radian is the angle at the centre of a circle made by an arc whose length equals the radius. A full turn is 2π2\pi2π radians, which is 360∘360^\circ360∘.

In simple words

The arc length is s=rθs = r\thetas=rθ when θ\thetaθ is in radians. To convert, π rad=180∘\pi\ \text{rad} = 180^\circπ rad=180∘, so 1 rad=180∘π≈57.3∘1\ \text{rad} = \dfrac{180^\circ}{\pi} \approx 57.3^\circ1 rad=π180∘​≈57.3∘. Calculus and physics use radians, because the formulas such as ddxsin⁡x=cos⁡x\dfrac{d}{dx}\sin x = \cos xdxd​sinx=cosx are simple only when the angle is in radians. Make sure your calculator is set to the right mode.

Example

60∘=60×π180=π3 rad60^\circ = 60 \times \dfrac{\pi}{180} = \dfrac{\pi}{3}\ \text{rad}60∘=60×180π​=3π​ rad. On a circle of radius 6 cm6\ \text{cm}6 cm, this angle cuts off an arc of length 6 cm×π3=6.28 cm6\ \text{cm} \times \dfrac{\pi}{3} = 6.28\ \text{cm}6 cm×3π​=6.28 cm.

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Related terms

  • Trigonometric Ratios

← All glossary terms

Learn it in

  1. Angles and Radian MeasureClass 11 to 12
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Practise

  1. A motor pulley of radius 4 cm turns at 1500 revolutions per minute…Hard
  2. A sprinkler throws water 7.5 m and turns back and forth through 110°…Medium
  3. The minute hand of a clock is 9 cm long…Medium
  4. Arcs of the same length in two different circles subtend 40° and 50° at their centres…Medium
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Quick questions

  1. A grinding wheel turns at 2400 revolutions per minute. What is its angular speed?Hard
  2. A car wheel of diameter 64 cm makes 750 revolutions without slipping. How far does the…Medium
  3. A sector of a circle of radius 12 cm has an arc of length 15 cm. What is the area of the…Medium

More Mathematics terms

  1. Algebraic Identity
  2. Arithmetic Progression
  3. Complex Number
  4. Derivative
  5. Function
  6. Isosceles Triangle
All Mathematics terms →

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