# Formulas and Tables

Trigonometry# Angle Measures

Angle measure in degrees: \(\alpha\)

Angle measure in radians: \(x\)

- 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.
- \(1\) degree contains \(60\) minutes of arc: \(1^\circ = 60’\). In turn, \(1\) arcminute has \(60\) arcseconds: \(1′ = 60^{\prime\prime}\).
- Value of \(1\) radian in degrees

\(1 \text{ rad } = 180^\circ/\pi\ \approx\) \( 57^\circ 17’45^{\prime\prime}\) - Value of \(1\) degree in radians

\(1^\circ = \pi/180 \text{ rad } \approx\) \( 0.017453 \text{ rad }\) - Value of \(1\) arcminute in radians

\(1′ = \pi /\left( {180 \cdot 60} \right) \text{ rad } \approx\) \( 0.000291 \text{ rad }\) - Value of \(1\) arcsecond in radians

\(1^{\prime\prime} = \pi /\left( {180 \cdot 3600} \right) \text{ rad } \approx\) \( 0.000005 \text{ rad }\) - Degrees to radians conversion \(x = \pi\alpha/{180^\circ},\)

where \(x\) is the angle value in radians, \(\alpha\) is the angle value in degrees. - Radians to degrees conversion \(\alpha = 180^\circ x/\pi,\)

where \(\alpha\) is the angle value in degrees, \(x\) is the angle value in radians. - Radian measures of common angles

### Related Pages

- Definition and Graphs of Trigonometric Functions
- Basic Trigonometric Identities
- Cofunction and Reduction Identities
- Relationships between Trigonometric Functions
- Addition and Subtraction Formulas
- Double and Multiple Angle Formulas
- Half-Angle Formulas
- Sum-to-Product Identities
- Product-to-Sum Identities
- Powers of Trigonometric Functions
- Inverse Trigonometric Functions