Answer
$\sin (-90^{\circ})=-1 \\ \cos (-90^{\circ})=0$ ; $\tan (-90^{\circ})=$ Not defined
and
$\csc (-90^{\circ})=-1$; $\sec (-90^{\circ})=$ Not defined ; $\cot (-90^{\circ})=0$
Work Step by Step
Here, the angle with $(0,-1)$ as a terminal point is: $-90^{\circ}=-270^{\circ}$
The Trigonometric functions are as follows:
$\sin (-90^{\circ})=-1 \\ \cos (-90^{\circ})=0$ ; $\tan (-90^{\circ})=$ Not defined
and
$\csc (-90^{\circ})=-1$; $\sec (-90^{\circ})=$ Not defined ; $\cot (-90^{\circ})=0$
