which represents an even function?\n$y = \\cos(x)$\n$y = \\sin(x)$\n$y = \\tan(x)$\n$y = \\cot(x)$

Explanation:

Step1: Recall the definition of an even function

An even function satisfies (f(-x)=f(x)) for all (x) in its domain.

Step2: Check (y = \cos(x))

We know that (\cos(-x)=\cos(x)). For example, if (x = \frac{\pi}{2}), (\cos\left(-\frac{\pi}{2}\right)=0) and (\cos\left(\frac{\pi}{2}\right)=0).

Step3: Check (y=\sin(x))

We know that (\sin(-x)=-\sin(x)). For example, if (x=\frac{\pi}{2}), (\sin\left(-\frac{\pi}{2}\right)= - 1) and (\sin\left(\frac{\pi}{2}\right)=1).

Step4: Check (y = \tan(x))

Since (\tan(x)=\frac{\sin(x)}{\cos(x)}), then (\tan(-x)=\frac{\sin(-x)}{\cos(-x)}=\frac{-\sin(x)}{\cos(x)}=-\tan(x)). For example, if (x = \frac{\pi}{4}), (\tan\left(-\frac{\pi}{4}\right)=-1) and (\tan\left(\frac{\pi}{4}\right)=1).

Step5: Check (y=\cot(x))

Since (\cot(x)=\frac{\cos(x)}{\sin(x)}), then (\cot(-x)=\frac{\cos(-x)}{\sin(-x)}=\frac{\cos(x)}{-\sin(x)}=-\cot(x)). For example, if (x=\frac{\pi}{4}), (\cot\left(-\frac{\pi}{4}\right)=-1) and (\cot\left(\frac{\pi}{4}\right)=1).

Answer:

(y = \cos(x))