NUMBAT OER - Open Educational Resources

5. Degrees and radians

We are used to measuring angles in degrees, where a right angle is 90°, the angle subtended by a straight line is 180° and a full revolution of a circle is 360°. We can also measure angles using a unit called a 'radian', which is based on the relationship between the circumference of a circle and its radius. Imagine an arc of a circle whose length is equal to the circle's radius. If you draw the radii at each end of the arc, the angle that they make at the centre of the circle is 1 radian. A full revolution of a circle is expressed as 2π radians, so:

90° = 0.5π radians
180° = 1π radians
270° = 1.5π radians
360° = 2π radians

Generally, if we have an angle measured in degrees, it can be converted to radians using the following formula:

α° = (α. π/180) radians

and conversely:

α radians = (α . 180/π)°

Note spreadsheets and many calculators use radians as the default measurement when calculating trigonometric functions. Thus SIN(2) returns the result 0.91, which is the sine of 2 radians, whereas the sine of 2° is 0.035. Triangles