f(x)=sin(-x)cos(-x) even odd or neither?

I believe this is part of a course where it is describing the "properties of functions." I worked on this sort of thing in January for my calc course. ;)

Calculate the problem f(-x); does it equal the same thing as f(x)? This means the function is "even."

If the answer you get is -f(x), the function is "odd."

f(-x) of the above = sin(--x)cos(--x) = sin(x)cos(x) So, f(x) does NOT = f(-x) the function is not even.

-f(x) = -[sin(-x)cos(-x)]

I'm not certain about the properties of sin & cos, but it LOOKS like f(-x) = -f(x) That would make this function odd.

Another way to look at it is to graph it. Even functions are symmetrical about the y-axis. Odd functions are symmetrical about the origin. Even functions look like there is a mirror on the y-axis. Odd functions look the same when you look at them upside-down.

Graphed this one on my calculator: this agrees with the function being odd: there's a hill on the upper left and a valley in the lower right that appear to be of the same proportions; if I turn my calculator upside-down, the graph looks the same.