Question

Find the value of trigonometric function $\text{cosec}(-{1410}^{\circ })$

Answer 1

It is known that the values of cosec⁡𝑥 repeat after an interval of $2\pi$ or ${360}^{\circ }$
$\therefore \text{cosec}(-{1410}^{\circ })=-\text{cosec}\left({1410}^{\circ }\right)\{\because \text{cosec}(-x)=-\text{cosec x}\}$
$=-\text{cosec}\left(4\right({360}^{\circ })-{30}^{\circ })$
$=-\left(\text{cosec}\right(-{30}^{\circ }\left)\right)$
$=-(-\text{cosec}{30}^{\circ })$
$=\text{cosec}{30}^{\circ }$
=2