Final answer:
Option (c) best illustrates why cosine is an even function, as it implies the cosine of an angle is equal to the cosine of the negative of that angle, reflecting the even function property of symmetry about the y-axis.
Step-by-step explanation:
The statement that illustrates why cosine is an even function is option (c), which states "cosine (startfraction 4 pi over 4 endfraction) cosine (negative startfraction pi over 4 endfraction) = cosine (startfraction 4 pi over 4 endfraction)". An even function is characterized by the property that f(x) = f(-x) for every x in the function's domain. In the context of the cosine function, this means that the cosine of an angle is the same as the cosine of the negative of that angle, because cosine is symmetrical about the y-axis. The correct expression illustrating this property is "cosine (-θ) = cosine (θ)" for all θ, which isn't explicitly shown in the options but can be inferred from option (c) if it is correctly stated as: "cosine (negative startfraction pi over 4 endfraction) = cosine (startfraction pi over 4 endfraction)".