Question

Which statement illustrates why cosine is an even function?

a) cosine (startfraction pi over 4 endfraction) = negative
b) cosine (startfraction 5 pi over 4 endfraction)
c) cosine (startfraction pi over 4 endfraction) = negative
d) cosine (startfraction 4 pi over 4 endfraction)

Answer 1

The statement that illustrates why cosine is an even function is option d) cosine (pi/4) = cosine(4pi/4). Cosine is an even function because its graph is symmetric about the y-axis.

Step-by-step explanation:

The statement that illustrates why cosine is an even function is option d) cosine ( pi/4 ) = cosine( 4pi/4 ).

To understand why cosine is an even function, we need to look at the cosine function graph. The graph of cosine is symmetric about the y-axis, which means that for any angle A, cosine(A) = cosine(-A). This is true because cosine is the x-coordinate value of a point on the unit circle. So, since cosine(pi/4) is the same as cosine(4pi/4), cosine is an even function.