Question

Find the value of $\mathrm{cosec}(-1410°).$

Answer 1

Finding the value of $\mathrm{cosec}(-1410°)$

$\begin{array}{rcl}\mathrm{cosec}(-1410°)& =& –\mathrm{cosec}(1410°)\\ & =& –\mathrm{cosec}(1440°–30°)\\ & =& –\mathrm{cosec}(4\times 360°–30°)\\ & =& –(–\mathrm{cosec}30°)\\ & =& \mathrm{cosec}30°\\ & =& \frac{1}{\sin 30°}\\ & =& \frac{1}{1/2}\\ & =& 2\end{array}$

Hence the value of $\mathrm{cosec}(-1410°)$ is $2$