Question:
Find the value of the trigonometric function $\operatorname{cosec}\left(-1410^{\circ}\right)$
Solution:
It is known that the values of $\operatorname{cosec} x$ repeat after an interval of $2 \pi$ or $360^{\circ}$.
$\therefore \operatorname{cosec}\left(-1410^{\circ}\right)=\operatorname{cosec}\left(-1410^{\circ}+4 \times 360^{\circ}\right)$
$=\operatorname{cosec}\left(-1410^{\circ}+1440^{\circ}\right)$
$=\operatorname{cosec} 30^{\circ}=2$