Step 1 :The cosecant function, \(csc(x)\), is defined as \(1/\sin(x)\). Therefore, to find the value of \(csc(-630°)\), we need to find the value of \(\sin(-630°)\) first.
Step 2 :The sine function has a period of 360°, which means \(\sin(x) = \sin(x + 360°n)\) for any integer n. Therefore, \(\sin(-630°) = \sin(-630° + 360°n) = \sin(90°) = 1\).
Step 3 :Then, \(csc(-630°) = 1/\sin(-630°) = 1/1 = 1\).
Step 4 :Final Answer: The value of \(\csc \left(-630^{\circ}\right)\) is \(\boxed{1}\).