Question

How do you convert $160$ degree into radians?

Answer 1

Hint:In order to convert the degree measure into radian measure ,multiply the given degree with $\dfrac{\pi }{{180}} radian $ to get your required result.

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${1^ \circ } = \dfrac{\pi }{{180}} radians$. This leads us to the standard to change over degree measure to radian measure. To change over from degree to radian, multiply the degree by $\dfrac{\pi }{{180}}radian$
So, in our question we are given ${330^ \circ }$
${1^ \circ } = \dfrac{\pi }{{180}}radians$
Multiplying both sides with ${160^ \circ }$.
\[
{1^ \circ } \times {160^ \circ } = \dfrac{\pi }{{180}} \times {160^ \circ }radians \\
{160^ \circ } = \dfrac{\pi }{9} \times 8\,radians \\
{160^ \circ } = \dfrac{{8\pi }}{9}radians \\
\]
Therefore, ${330^ \circ }$ into radians equal to \[\dfrac{{8\pi }}{9} radians\].

Alternate:
You can alternatively determine the answer by simply multiplying the given degree measure with $\dfrac{\pi }{{180}}radian$ in order to convert into radian
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.Standard International (SI) to measure any angle is radian.
3.Place the units carefully.