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Radian

1.1 Radian
 
The image is a diagram explaining the conversion between radians and degrees. At the top, there is a dark blue box labeled ‘RADIAN’ with the Pandai logo above it. Below this box, an arrow points to a central box labeled ‘Conversion Formula,’ which states ‘π rad = 180°’. From this central box, two arrows branch out. The left arrow points to a light blue box labeled ‘to degrees,’ showing the formula ‘x rad × 180°/π’. The right arrow points to another light blue box labeled ‘to radians,’ showing the formula ‘x° × π/180°’.
 
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

A triangle representing 1 radian where the radius matches the arc length.
 
Relationship with Degrees
  • \(1\text{ rad}=\dfrac{180^\circ}{\pi}\)
  • \(360^\circ=2\pi \text{ rad}\)
 
Conversion Formula
  • To convert degrees to radians:

\(\text{radians}=\text{degrees}\times \dfrac{\pi}{180^\circ}\)

  • To convert radians to degrees:

\(\text{degrees}=\text{radians}\times\dfrac{180^\circ}{\pi}\)
 
Example \(1\)
Question

Convert \(120^\circ\) to radians.
Solution

\(\begin{aligned} \text{radians}&=120^\circ\times\dfrac{\pi}{180^\circ} \\\\ &=\dfrac{2\pi}{3}\text{ rad} .\end{aligned}\)
 
Example \(2\)
Question

Convert \(\dfrac{\pi}{4}\text{ rad}\) to degrees.
Solution

\(\begin{aligned} \text{degrees}&=\dfrac{\pi}{4}\text{ rad}\times\dfrac{180^\circ}{\pi} \\\\ &=45^\circ. \end{aligned}\)
 
The views expressed in the notes here are those of the contributor and don’t necessarily represent the views of pandai.

Radian

1.1 Radian
 
The image is a diagram explaining the conversion between radians and degrees. At the top, there is a dark blue box labeled ‘RADIAN’ with the Pandai logo above it. Below this box, an arrow points to a central box labeled ‘Conversion Formula,’ which states ‘π rad = 180°’. From this central box, two arrows branch out. The left arrow points to a light blue box labeled ‘to degrees,’ showing the formula ‘x rad × 180°/π’. The right arrow points to another light blue box labeled ‘to radians,’ showing the formula ‘x° × π/180°’.
 
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

A triangle representing 1 radian where the radius matches the arc length.
 
Relationship with Degrees
  • \(1\text{ rad}=\dfrac{180^\circ}{\pi}\)
  • \(360^\circ=2\pi \text{ rad}\)
 
Conversion Formula
  • To convert degrees to radians:

\(\text{radians}=\text{degrees}\times \dfrac{\pi}{180^\circ}\)

  • To convert radians to degrees:

\(\text{degrees}=\text{radians}\times\dfrac{180^\circ}{\pi}\)
 
Example \(1\)
Question

Convert \(120^\circ\) to radians.
Solution

\(\begin{aligned} \text{radians}&=120^\circ\times\dfrac{\pi}{180^\circ} \\\\ &=\dfrac{2\pi}{3}\text{ rad} .\end{aligned}\)
 
Example \(2\)
Question

Convert \(\dfrac{\pi}{4}\text{ rad}\) to degrees.
Solution

\(\begin{aligned} \text{degrees}&=\dfrac{\pi}{4}\text{ rad}\times\dfrac{180^\circ}{\pi} \\\\ &=45^\circ. \end{aligned}\)
 
The views expressed in the notes here are those of the contributor and don’t necessarily represent the views of pandai.
Chapter : Circular Measure
Topic : Radian
Form 5 Additional Mathematics
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