Question

HELPPPP!!! Select the correct answer. Which function is an even function?

Answer 1

Answer:

C.

Step-by-step explanation:

p(x)=sin(x) is an odd function since sin(-x)=-sin(x).

q(x)=cos(x) is an even function since cos(-x)=cos(x).

r(x)=tan(x) is an odd function since tan(-x)=-tan(x).

s(x)=csc(x) is an odd function since csc(-x)=-csc(x).

So the only contender seems to be C.

Let's check.  To check we have to plug in (-x) in place of (x) and see if we get the same function back since we are looking for an even function.

$f(x)=\cos(\frac{5\pi}{4}x)$

Replace (x) with (-x):

$f(-x)=\cos(\frac{5\pi}{4}(-x)$

$f(-x)=\cos(\frac{-5\pi}{4}x)$

$f(x)=\cos(\frac{5\pi}{4}x)$ since cosine is even; that is cos(-u)=cos(u) where u in this case is $\frac{5\pi}{4}x$.

So f is even.