Question

Using the definition of an even function, show that y = -cos(x) is even.

A. Symmetry with respect to the y-axis
B. Symmetry with respect to the x-axis
C. Symmetry with respect to the origin
D. No symmetry

Answer 1

The function y = -cos(x) is even and is symmetric with respect to the y-axis.

Step-by-step explanation:

An even function is a function that satisfies the condition y(x) = y(-x). To show that y = -cos(x) is even, we can substitute -x for x and show that y(-x) = y(x).

Let's substitute -x for x in the given function: y(-x) = -cos(-x). Using the identity cos(-x) = cos(x), we can simplify this to y(-x) = -cos(x).

Comparing this with the original function y(x) = -cos(x), we can see that y(-x) = y(x). Therefore, the function y = -cos(x) satisfies the condition for even functions and is symmetric with respect to the y-axis.