Could someone help me understand even and odd functions?

Question

I missed class today due to a doctor's appointment and I have a quiz over this tomorrow.

From what I know, odd functions are -f (x) = f (-x), and even is f (x) = f (-x).

Poblem one says to find the sin of 30 degrees and sin of -30 degrees. After that test them and see if it is even or odd. I don't understand how to test them. I can find the sine values, but I don't know what to do with them. What makes a function even or odd?

Answer 1

Test them against the definitions of even and odd functions:

1. odd function is -f (x) = f (-x)
2. even is f (x) = f (-x)

If -sin(30°) = sin(-30°), then by the definition it is odd. If sin(30°) = sin(-30°), then by the definition the sine function is even. If it is neither, then it's neither even nor odd.