Question

Convert $6$ radians into degree measure.

Answer 1

Hint: We measure angles using the units degrees and radian.
A circle is made of $360$ degrees. This ${{360}^{{}^\circ }}$ is also equal to $2\pi$ radians where the value of $\pi$ is $3.14159$. That means $2\pi$ radians =${{360}^{{}^\circ }}$
Hence, $1\pi$ radian is ${180}^\circ$. Here, $\pi$ radian means a semicircle.

Complete step-by-step solution -
If ${{180}^{{}^\circ }}$ is equal to $1\pi$, then the value of the $1$ degree will be given as $\dfrac{\pi }{180}$ or the value of $1$ radian is $\dfrac{180}{\pi }$
radian $=\dfrac{180}{\pi }$ degrees
Therefore to convert any radian to degree, we multiply the given radian by $\dfrac{180}{\pi }$
The formula to convert radian into degrees is
degrees = radians $\times \dfrac{{{180}^{{}^\circ }}}{\pi }$
In the given question, $6$ radians are given
The value of radians in degrees will be converted as,
$\Rightarrow 6\times \dfrac{{{180}^{\circ }}}{\pi }=6\times \dfrac{180\times 7}{22}$. \left\\{ \therefore \pi =\dfrac{22}{7} \right\\}
$\Rightarrow {{343.7746}^{\circ }}$
Answer is $6$ radians $=343.7746{}^\circ$.

Note: To convert from degrees to radians, we multiply the given degree by $\dfrac{\pi }{180}$. The degree is measured by the amount of tiltness in an angle whereas radians is measured by the amount of distance traveled by the angle given as (arc length/radius).