Final answer:
The correct answer is D. f(t) = csc(-x).
Step-by-step explanation:
An even function is a function that satisfies the property f(x) = f(-x) for all x in the domain. Using this definition, we can determine which of the given functions is even:
A. f(1) = sin(-37x) - This is not an even function because sin function is not equal to its negative value.
B. f(x) = tan(3x) - This is not an even function because the tangent function is not symmetric about the y-axis.
C. f(3) = cos(5x) - This is not an even function because cos function is not equal to its negative value.
D. f(t) = csc(-x) - This is an even function because the cosecant function is symmetric about the y-axis, meaning that f(x) = f(-x).
Therefore, the correct answer is D. f(t) = csc(-x).