Question

What is \[-\dfrac{3\pi }{8}\] radians in degrees?

Answer 1

Hint: In this problem, we have to convert \[-\dfrac{3\pi }{8}\] from radians to degree. We know that to convert the value of radian to its equivalent angle in degrees we should multiply the given value with \[\dfrac{{{180}^{\circ }}}{\pi }\] as the value of 180 degrees is \[\pi \] in radians. We can also use the exact value of radian to multiply with the given number to find the answer.

Complete step by step answer:
We know that the given radian is \[-\dfrac{3\pi }{8}\].
We should convert the given radian to its equivalent angle in degrees
We should know that, one complete revolution counter clockwise in an XY plane will be equal to \[2\pi \](in radians) or 360 (in degrees), so we can write
\[\begin{align}
  & 2\pi ={{360}^{\circ }} \\
 & \pi rad={{180}^{\circ }} \\
 & rad=\dfrac{{{180}^{\circ }}}{\pi } \\
\end{align}\]
If we want to convert the value of radian to its equivalent angle in degrees, we should multiply the given value with \[\dfrac{{{180}^{\circ }}}{\pi }\].
We can multiply the given \[-\dfrac{3\pi }{8}\] value with \[\dfrac{{{180}^{\circ }}}{\pi }\], we get
\[\Rightarrow -\dfrac{3\pi }{8}\times \dfrac{{{180}^{\circ }}}{\pi }\]
We can now simplify the above term by cancelling the similar terms and multiplying the remaining terms, we get
\[\Rightarrow -\dfrac{3\pi }{8}\times \dfrac{{{180}^{\circ }}}{\pi }=-67.5\]degrees.

Therefore, the answer is -67.5 degrees.

Note: We should know that why we multiply the given number with \[\dfrac{\pi }{{{180}^{\circ }}}\] to convert into its radians or \[\dfrac{{{180}^{\circ }}}{\pi }\] to convert into its degrees as the value of 180 degrees is \[\pi \] in radians. We should also concentrate on the multiplication part as we can take \[\pi \] as 3.14 or \[\dfrac{22}{7}\] either we can use calculators.