Question

How do you convert 1radian into degree?

Answer 1

Hint:In order to convert the radian measure into degree measure ,multiply the given radian with $\dfrac{{180}}{\pi }\,$degree to get your required result. Remember one thing that the Standard international (SI) unit of measure of any angle is radian not degree.$\pi $is a constant term having value equal to $\dfrac{{22}}{7}\,or\,3.14\,approx$.

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 conditions
${360^ \circ } = 2\pi \,radians$ and
${180^ \circ } = \pi $ radians

From the last mentioned, we get the condition$1\,radian = \dfrac{{{{180}^ \circ }}}{\pi }\deg ree$.

This leads us to the standard to change over radian measure to degree measure. To change over from radian to degree, multiply the radian by $\dfrac{{180}}{\pi }\,$degree.

So, in our question we are given 1 radian
$1\,radian = \dfrac{{{{180}^ \circ }}}{\pi }$degree

Putting value of $\pi = 3.14$
$1\,radian = \dfrac{{180}}{{3.14}}\,$degree
$1\,radian = {57.3248^ \circ }$degree

Rounding off up to 1 decimal place
$1\,radian = {57.3^ \circ }$

So, if we want to convert 5 radian to degree then multiply $5\,radian =
\dfrac{{180}}{{3.14}}\,$degree
=$5 \times \dfrac{{180}}{\pi }\,$degree
=$\dfrac{{900}}{{3.14}}$ degree

Therefore,5 radian into degree is equal to${286.6^ \circ }$.

Additional Information: 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 $\dfrac{{180}}{\pi }$degrees or just we can say of ${57.3^ \circ }$.

The unit was once in the past a SI supplementary unit (before that classification was nullified in 1995) and the radian is currently viewed as a SI derived unit.

The radian is characterized in the SI similar to a dimensionless value, and its image is appropriately regularly discarded, particularly in mathematical writing.

Note:1. Don’t forget to Cross-check your answer.
2.SI unit of measure of any angle is radian.
3.Carefully write the units