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Angle measurement

What's an Angle?

Check this short to understand an Angle: what's an Angle?

Degrees

Degrees are a unit of angle measurement commonly used in everyday situations.

  • Degrees: A full rotation around a circle is divided into 360 equal parts, each part being 1 degree. Denoted by: the symbol \(^\circ\).

  • Minutes: Each degree is further divided into 60 equal parts, called minutes. Denoted by: the symbol \('\).

  • Seconds: Each minute is further divided into 60 equal parts, called seconds. Denoted by: the symbol \(''\).

Radians

Radians are an alternative unit of angle measurement often used in mathematical contexts, particularly in calculus and trigonometry. One radian is the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle. $$ \text{Radians} = \frac{\text{Arc Length}}{\text{Radius}} $$

One full revolution is \(2\pi\) radians.

Systems of Measurement of an Angle

Check this short to understand: Systems of Measurement of an Angle

Conversion formula

The following formulas to convert between degrees and radians:

  • To convert degrees to radians: $$ \text{Radians} = \frac{\text{Degrees} \times \pi}{180} $$

  • To convert radians to degrees: $$ \text{Degrees} = \frac{\text{Radians} \times 180}{\pi} $$

Conversion between Degrees & Radians

Check this short to understand: Conversion between Degrees & Radians