Answer
$sin\frac{9\pi}{2}=1$
$cos\frac{9\pi}{2}=0$
$tan\frac{9\pi}{2}= undefined$
$csc\frac{9\pi}{2}=1$
$sec\frac{9\pi}{2}=undefined$
$cot\frac{9\pi}{2}=0$
Work Step by Step
Since, $\frac{9\pi}{2}$ is coterminal angle with $\frac{\pi}{2}$ i.e at positive y-axis, which can be considered as common angle to all trigonometric ratios.
The trigonometric ratios and their inverse trigonometric ratios are given as follows:
$sin\frac{9\pi}{2}=sin\frac{\pi}{2}=1$
$cos\frac{9\pi}{2}=cos\frac{\pi}{2}=0$
$tan\frac{9\pi}{2}=tan\frac{\pi}{2} = undefined$
$csc\frac{9\pi}{2}=\frac{1}{sin\frac{9\pi}{2}}=1$
$sec\frac{9\pi}{2}=\frac{1}{cos\frac{9\pi}{2}}=undefined$
$cot\frac{9\pi}{2}=\frac{1}{tan\frac{9\pi}{2}}=0$
