Is cos x even or odd?

Trigonometry is the branch of maths that deals with relationships between sides and angles of various geometrical objects.

Answer: Cos x is an even function.

Let's understand the solution in detail.

Explanation:

To check for odd function, we need to verify if f(-x) = -f(x) for all x, and to check for even functions we check if it follows the relation f(-x) = f(x) for all x.

Now, we check this for cos x:

⇒ f(x) = cos x

Since cos x is positive in the first and the fourth quadrant and -x is the angle from positive the x-axis in a clockwise direction, hence lying in the fourth quadrant.

⇒ f(-x) = cos (-x) = cos x  

Hence, we see that f(-x) = f(x).

Therefore, cos x is an even function.