Are the functions :
(i) f(x) = cos x
(ii) f(x) sin x
even functions or odd functions and why?
(i) f(x) = cos x is an even function because it satisfies the property f(x) = f(-x) for all x. In other words, the function is symmetric about the y-axis.
(ii) f(x) = sin x is an odd function because it satisfies the property f(x) = -f(-x) for all x. In other words, the function is symmetric about the origin.