Question

How do you find an angle between \[0\] and \[2\pi \] that is coterminal with \[ - \dfrac{{19\pi }}{{24}}\] express answer in radians?

Answer 1

Hint: To find the coterminal angle we need to add or subtract from a given angle. If the given angle is greater than \[2\pi \], then we subtract \[2\pi \] from the given angle. If the given angle is less than \[2\pi \], then we add \[2\pi \] to the given angle.

Complete step by step solution:
Coterminal angles are angles in standard position that have common terminal sides. We have to find an angle between \[0\] and \[2\pi \], which is coterminal with \[ - \dfrac{{19\pi }}{{24}}\].
Here we have \[ - \dfrac{{19\pi }}{{24}}\], which is equal to:
\[ - \dfrac{{19\pi }}{{24}}\] \[ = \] \[ - 0.79\pi \]
So, this is less than \[2\pi \].
So we have to add \[2\pi \]to it:
\[\therefore \] \[ - \dfrac{{19\pi }}{{24}}\] \[ + \] \[2\pi \]
Taking L.C.M. we get,
\[ = \dfrac{{ - 19\pi + 48\pi }}{{24}}\]
\[ = \dfrac{{29\pi }}{{24}}\]
So \[\dfrac{{29\pi }}{{24}}\] is coterminal angle with\[ - \dfrac{{19\pi }}{{24}}\].

Note: Remember the rule that if the given angle is is greater than \[2\pi \], then we subtract \[2\pi \] from the given angle and if the given angle if less than \[2\pi \], then we add \[2\pi \] to the given angle, to find its coterminal angle. This is applicable if the angles are in radians. If the angle is in degree then add \[{360^ \circ }\] to the angle if the angle is less than \[{360^ \circ }\], ad subtract \[{360^ \circ }\] from the angle if the angle is greater than \[{360^ \circ }\], to find its coterminal angle.