What is the radian measure of an angle of x degrees?
Answer: The radian measure of an angle of x degrees is equal to xπ / 180 radians.
An angle at which the terminal side is along the negative x-axis is measured in radians.
1 radian is defined as the angle subtended at the centre of a unit circle by a unit arc length on the circumference.
An arc length of 't' units subtends an angle measure of 't' radians at the centre of the circle as shown in the diagram below.
Since the circumference of a unit circle is 2π units, we have,
360º = 2π radians
⇒ 180º = π radians
Hence, one radian is equal to 180 / π degrees, which is approximately 57.3º
Thus, we have the conversion formulas as follows:
- Multiply the angle by π /180 to convert from degrees to radians.
Multiply the angle by 180/ π to convert from radians to degrees.
To convert x degrees to radian we will multiply x with π /180
Thus, x degrees = xπ /180 radians