Question

How do you convert \[\dfrac{{5\pi }}{7}\] from radians to degree?

Answer 1

Hint: The radians measure of any angle is given by, \[\theta = \dfrac{l}{r}\] . Here \[l\] is the length of the arc around the angle and \[r\] is the radius of the circle.

Complete step-by-step answer:
The radian measure of any angle is given by, \[\theta = \dfrac{l}{r}\] . Here \[l\] is the length of the arc around the angle and \[r\] is the radius of the circle. So, now when we consider angle formed when tracing the entire circle once, in the degrees measure it is \[360^\circ \] . Also, \[l = 2\pi r\] in this case. So, the radians measure would be \[\theta = \dfrac{{2\pi r}}{r} = 2\pi \] .
Hence, \[2\pi = 360^\circ \] . So, the value of \[180^\circ \] is the same as \[\pi \] radians.
Using the above given relation between \[\pi \] and degrees we can see that for converting a given angle from its radians measure to the measurement of degrees, one needs to multiply the value by \[\dfrac{{180}}{\pi }\] .
So, angle in degrees \[ = \] angle in radians \[ \times \] \[\dfrac{{180}}{\pi }\] .
And, the value of \[\pi \] is usually taken as \[\dfrac{{22}}{7}\] or \[3.14\] .
Now the angle is given in the radians measure as \[\dfrac{{5\pi }}{7}\] .
So, the angle measure in degrees is given by, \[\dfrac{{5\pi }}{7} \times \dfrac{{180}}{\pi } = \dfrac{{5 \times 180}}{7} = 128.57^\circ \]
Hence, \[\dfrac{{5\pi }}{7}\] radians is equal to \[128.57^\circ \] .
So, the correct answer is “ \[128.57^\circ \] ”.

Note: Angle measurements are measured in degrees and radians, which are two distinct units. When determining angles in Geometry, the conversion of degrees to radians is taken into account. The angle is usually measured in degrees, which is shown by the symbol \[^\circ \] . Degrees and radians are two separate types of units that can be used to measure an angle. Using simple formulas, you can convert one form of the representation of any mathematical angle to the other. Minutes and seconds are the further subdivisions of a degree. Trigonometry applications depend heavily on this conversion.
The angle formed when the radius is wrapped around the circle is given as \[1\] radian and \[1\] radian is approximated to around \[57.2958^\circ \] .