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).