Question

$cosec(-1410)$.

Answer 1

Here, we have, $\theta =1410$

also, $\theta =2n\pi +\alpha$

where $n=\left[\frac{\theta }{2\pi }\right]$

$n=\left[\frac{-1410}{2\left(180\right)}\right]=-4$

So, $\alpha =-2n\pi +\theta$

$=-2(-4)\left(180\right)+(-1410)$

$\alpha =30$

So, $cosec\left(\theta \right)=cosec(2n\pi +\alpha )$

$=cosec\alpha$

$=cosec\left(30\right)$

$=cosec30$

$cosec(-1410)=2$