Formulas and Tables

Trigonometry

Angle Measures

Angle measure in degrees: \(\alpha\)

Angle measure in radians: \(x\)

  1. There are two commonly used units for measuring angles − degrees and radians. \(1\) degree (denoted by \(1^\circ \)) is defined as\(1/360\) of a complete revolution. The straight angle is equal to\(180^\circ \), the right angle is \(90^\circ \). The radian measure of an angle whose vertex lies at the centre of a circle is the ratio of the arc length to the radius of the circle. A central angle is equal to \(1\) radian (denoted as \(1 \text{ rad }\)) if the angle subtends an arc whose length is equal to the radius of the circle.
  2. \(1\) degree contains \(60\) minutes of arc: \(1^\circ = 60’\). In turn, \(1\) arcminute has \(60\) arcseconds: \(1′ = 60^{\prime\prime}\).
  3. Value of \(1\) radian in degrees
    \(1 \text{ rad } = 180^\circ/\pi\ \approx\) \( 57^\circ 17’45^{\prime\prime}\)
  4. Value of \(1\) degree in radians
    \(1^\circ = \pi/180 \text{ rad } \approx\) \( 0.017453 \text{ rad }\)
  5. Value of \(1\) arcminute in radians
    \(1′ = \pi /\left( {180 \cdot 60} \right) \text{ rad } \approx\) \( 0.000291 \text{ rad }\)
  6. Value of \(1\) arcsecond in radians
    \(1^{\prime\prime} = \pi /\left( {180 \cdot 3600} \right) \text{ rad } \approx\) \( 0.000005 \text{ rad }\)
  7. Degrees to radians conversion \(x = \pi\alpha/{180^\circ},\)
    where \(x\) is the angle value in radians, \(\alpha\) is the angle value in degrees.
  8. Radians to degrees conversion \(\alpha = 180^\circ x/\pi,\)
    where \(\alpha\) is the angle value in degrees, \(x\) is the angle value in radians.
  9. Radian measures of common angles
Radian measures of common angles