Question

How many radians does it take to go $720$ degrees ?

Answer 1

Hint: In the given question, we are required to convert the angle given in degree measure into radian measure. Radian is the SI unit for measuring angles. In order to convert the degree measure into radian measure, multiply the given degree measure with $\left[ {\dfrac{\pi }{{180}}} \right]$ to get the desired result.

Complete step by step answer:
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 $360$degrees. Along these lines, degree measure and radian measure are connected by the conditions:
$2\pi $radians $ = {360^ \circ }$
$\Rightarrow\pi $radians $ = {180^ \circ }$
From the above mentioned equations or results, we get the condition $1$ radian $ = \dfrac{{180}}{\pi }$degrees. This leads us to the standard to change over degree measure to radian measure. To change over from degree to radian, we multiply the degree measure by $\dfrac{\pi }{{180}}$.So, in our question we are given ${330^ \circ }$.Multiplying both sides with ${330^ \circ }$.
${720^ \circ } = \dfrac{{720\pi }}{{180}}$radians
Cancelling the common factors in numerator and denominator, we get,
$ \therefore {720^ \circ } = 4\pi $radians

Therefore, ${720^ \circ }$ in radians equal to $4\pi $ 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 $\dfrac{{180}}{\pi }$ degrees. Don’t forget to Cross-check your answer.