Find the indicated function value. If it is undefined, say so.
\[
\csc \left(-630^{\circ}\right)
\]
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. $\csc \left(-630^{\circ}\right)=$
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
B. The function is undefined.
Answer
Final Answer: The value of \(\csc \left(-630^{\circ}\right)\) is \(\boxed{1}\).
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 \(\boxed{1}\).
