Answer:
[tex]\dfrac{\pi}{10}[/tex].
Step-by-step explanation:
All coterminal angles of an angle [tex]\theta[/tex] are defined as
[tex]\theta +2n\pi[/tex] or [tex]\theta + n360^{\circ}[/tex]
where, n is an integer.
The given angle is
[tex]\theta=-\dfrac{19\pi}{10}[/tex]
So, all coterminal angles of an angle [tex]\theta[/tex] are
[tex]-\dfrac{19\pi}{10}+2n\pi[/tex]
For n=1,
[tex]\Rightarrow -\dfrac{19\pi}{10}+2(1)\pi[/tex]
[tex]\Rightarrow -\dfrac{19\pi}{10}+2\pi[/tex]
[tex]\Rightarrow \dfrac{-19\pi+20\pi}{10}[/tex]
[tex]\Rightarrow \dfrac{1\pi}{10}[/tex]
Since, [tex]\dfrac{\pi}{10}[/tex] between 0 and 2π, therefore, the required coterminal angle is [tex]\dfrac{\pi}{10}[/tex].
