Answer
$\sin(270^{o})=-1$
$\cos(270^{o})= 0$
$\tan(270^{o})$ is not defined
$\csc(270^{o})=-1$
$\sec(270^{o})$ is not defined
$\cot(270^{o})=0$
Work Step by Step
Reference Angle $\theta^{\prime}$ for $\theta$ in $(0^{\mathrm{o}},\ 360^{\mathrm{o}})$
$\left[\begin{array}{lllll}
Quadrant: & I & II & III & IV\\
\theta' & \theta & 180^{o}-\theta & \theta-180^{o} & 360^{o}-\theta
\end{array}\right]$
$990^{o}$ is coterminal with the angle
$990^{o} -2\cdot 360^{o}=990^{o} -720^{o}=270^{o}$
for which the reference angle is
$\theta^{\prime}=\theta-180^{o}=270^{o}-180^{o}=90^{o}$
At $90^{o}$ ,tan and sec are not defined,
cos and cot are 0
sin and csc are 1.
So
$\sin(270^{o})=-1$
$\cos(270^{o})= 0$
$\tan(270^{o})$ is not defined
$\csc(270^{o})=-1$
$\sec(270^{o})$ is not defined
$\cot(270^{o})=0$
