Question

How do you convert $120$ degrees into radians?

Answer 1

Hint: In order to convert the degree measure into radian measure, multiply the given degree measure with $\left( {\dfrac{\pi }{{180}}} \right)$ radians to get the required result. Radian describes the plane angle subtended by a circular arc, as the length of the arc divided by the radius of the arc. One radian is the angle subtended at the centre of a circle by an arc that is equal in length to the radius of the circle.

Complete step by step solution:
The measure of an angle is controlled by the measure of pivot from the underlying side to the terminal side. In radians, one complete counter clockwise upheaval is $2\pi $ and in degrees, one complete counterclockwise upset is ${360^ \circ }$. Along these lines, degree measure and radian measure are connected by the condition:
${360^ \circ } = 2\pi $ radians
The above condition can also be simplified as follows:
${180^ \circ } = \pi $ radians
So, we get the condition ${1^ \circ } = \left( {\dfrac{\pi }{{180}}} \right)$ radians. This leads us to the standard to change over degree measure to radian measure. To change over from degree to radian, multiply the degree measure by $\left( {\dfrac{\pi }{{180}}} \right)$ radians.
So, in the question we are given $120$ degrees.
${1^ \circ } = \left( {\dfrac{\pi }{{180}}} \right)$ radians
Multiplying both sides of the equation with $120$.
${120^ \circ } = \left( {\dfrac{\pi }{{180}}} \right) \times 120$ radians
So, ${120^ \circ } = \left( {\dfrac{{2\pi }}{3}} \right)$ radians.
Therefore, $120$ degrees equal to $\left( {\dfrac{{2\pi }}{3}} \right)$ radians.

Note: The radian, indicated by the symbol $rad$, is the SI unit for measuring angles, and is the standard unit of angle measure utilized in numerous zones of arithmetic. The length of an arc of a unit circle is mathematically equivalent to the measurement in radians of the angle that it subtends; one radian is $\left( {\dfrac{{180}}{\pi }} \right)$ degrees. The radian is characterized in the SI similar to a dimensionless value