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.
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.