An even function is a function that satisfies the equality f(-x)=f(x) for all values of x. Is the cosine function an even function? Explain.
Yes, the cosine function is an even function. It satisfies the property of even functions, which is f(-x) = f(x) for all values of x.
In the case of the cosine function, we have cos(-x) = cos(x) for all values of x. This can be easily shown using the properties of cosine.
For any angle x, the cosine function gives the ratio of the adjacent side to the hypotenuse in a right triangle with angle x. Since the adjacent side remains unchanged when we go from x to -x, the ratio and thus the cosine value also remain unchanged.
Hence, the cosine function is symmetric about the y-axis and satisfies the property of even functions.