Is the cosine function even, odd, or neither? Is its graph symmetric? With respect to what?
Is the cosine function even, odd, or neither?
The cosine function is even.
Is the graph of the cosine function symmetric? With respect to what?
No. It is not symmetric.
Yes. It is symmetric with respect to the $y$-axis.
Yes. It is symmetric with respect to the $x$-axis.
Yes, It is symmetric with respect to the origin.
Answer
Therefore, the cosine function is even and its graph is symmetric with respect to the y-axis.
Step 1 ：The cosine function is an even function, which means that \(\cos(x) = \cos(-x)\) for all x.
Step 2 ：The graph of the cosine function is symmetric with respect to the y-axis, which is the line of symmetry for the graph of the cosine function.
Step 3 ：The graph of the cosine function is not symmetric with respect to the x-axis or the origin, because the values of the cosine function do not mirror across the x-axis or the origin.
Step 4 ：Therefore, the cosine function is even and its graph is symmetric with respect to the y-axis.
