Find the value of the trigonometric function cosec (–1410°)

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 $360^{\circ}$.

$\therefore \operatorname{cosec}\left(-1410^{\circ}\right)=\operatorname{cosec}\left(-1410^{\circ}+4 \times 360^{\circ}\right)$

$=\operatorname{cosec}\left(-1410^{\circ}+1440^{\circ}\right)$

$=\operatorname{cosec} 30^{\circ}=2$

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