Question

Find the degree measure corresponding to the following radian measure ( use $\pi = \dfrac{{22}}{7}$)
The angle in radian measure is ${\left( {\dfrac{{18\pi }}{5}} \right)^c}$

Answer 1

Hint: To convert an angle into degree measure from the corresponding radian measure we multiply by a factor of $\dfrac{{180}}{\pi }$ and to convert an angle into a radian measure from the corresponding degree measure we have to multiply angle in degree by a factor of $\dfrac{\pi }{{180}}$ .

Complete step-by-step answer:
The given radian measure of angle is ${\left( {\dfrac{{18\pi }}{5}} \right)^c}$
We know that ${180^o}$ is equal to ${\pi^c}$.
So, using the concept of unitary method unit angle in radian ${1^c}$ is equal to ${\left( {\dfrac{{180}}{\pi }} \right)^o}$
In the same way the value of angle in degree of radian measure ${x^c}$is\[{\left( {\dfrac{{180x}}{\pi }} \right)^o}\].
The degree measure of the angle ${\left( {\dfrac{{18\pi }}{5}} \right)^c}$given in radian measure is given by
Angle in degree measure is,
$
  A = {\left( {\dfrac{{18\pi }}{5} \times \dfrac{{180}}{\pi }} \right)^o} \\
  A = {648^o} \;
$
Hence, the angle in degree measure is ${648^o}$ for the angle ${\left( {\dfrac{{18\pi }}{5}} \right)^c}$ in radian measure.

Note: The important step is to know the factor for conversion in degree measure from the corresponding radian measure and vice versa.
If the angle is given in degree it is written as ${30^o}$ ,${60^o}$ , etc.
If the angle is given in radian measure it is written as $\dfrac{\pi }{6}$ ,$\dfrac{\pi }{3}$ etc.
The angle is measured in most commonly two units. They are namely,
I.Radian measure
II.Degree measure
The circumference of the circle of unit radius is $2\pi $ radian which is equal to${360^o}$ or we can also say that $\pi $ radian is equal to ${180^o}$ using the concept of unitary measure.
For instance, the value of $\sin \left( {{{30}^o}} \right) = \sin \left( {\dfrac{\pi }{6}} \right) = \dfrac{1}{2}$ and the value of$\cos \left( {{{60}^o}} \right) = \cos \left( {\dfrac{\pi }{3}} \right) = \dfrac{1}{2}$.