Question

What is \[\dfrac{{9\pi }}{8}\] radians in degrees?

Answer 1

Hint: The measurement of angles can be done in two different units namely radian and degree. In geometry, we measure the angles in degrees but also in radians sometimes, similarly in trigonometry, we measure the angle in radians but sometimes in degrees too. So, there are different kinds of units for determining the angle that are, degrees and radians. There is a simple formula to convert a given radian into degree (vice versa). Using that formula, we can find out the correct answer.

Complete step by step solution:
We know that the radian is denoted by ‘rad’.
We need to convert \[\dfrac{{9\pi }}{8}\] rad into degrees.
The value of \[\pi \] radian is equal to \[{180^0}\].
Then 1 rad is equal to \[\dfrac{{180}}{\pi }\] degrees.
So the given \[x\] rad is equal to \[x \times \dfrac{{180}}{\pi }\] degrees.
This is the general formula for converting the angle in radians to degrees.
Then \[\dfrac{{9\pi }}{8}\] rad becomes
\[\dfrac{{9\pi }}{8} = \dfrac{{9\pi }}{8} \times \dfrac{{180}}{\pi }\] degree
\[ = \dfrac{{9 \times 180}}{8}\]
\[ = \dfrac{{9 \times 45}}{2}\]
\[ = \dfrac{{405}}{2}\]
\[ = {202.5^0}\].
Hence \[\dfrac{{9\pi }}{8}\]rad is equal to \[{202.5^0}\].

Note:
Suppose lets say that they asked us to convert \[{202.5^0}\] into radians. Then
The value of \[{180^0}\] is equal to \[\pi \]radians.
Then \[{1^0}\] is equal to \[\dfrac{\pi }{{180}}\] radians.
So the given \[{x^0}\] is equal to \[x \times \dfrac{\pi }{{180}}\] radians.
This is the general formula for converting the angel in degrees to radians.
Now We have, \[{202.5^0}\], then
\[{202.5^0} = 202.5 \times \dfrac{\pi }{{180}}{\text{ radians}}\]
\[ = \dfrac{{202.5\pi }}{{180}}\].
Multiply numerator and the denominator by 10
\[ = \dfrac{{20250\pi }}{{1800}}\]
Divide numerator and the denominator by 227 we have
\[ = \dfrac{{9\pi }}{8}\].
Hence \[{202.5^0}\] is \[\dfrac{{9\pi }}{8}\] rad. If we observe the above answer, we can tell that the obtained answer is correct.