Question

The fact that sin(150°) = .5 and sin(-150°) = -.5 implies that the sine function is which type of function?

Answer 1

A) odd
B) even
C) neither
D) cannot be determined

Answer 2

even functions have this property: f(-x) = f(x)
odd functions have this property: f(-x) = -f(x)

Answer 3

If we take this first equation they gave us, multiply it by -1,
then we get these two equations,\[\large\rm -\sin(150)=-\frac12,\qquad\qquad\qquad \sin(-150)=-\frac12\]

They both equal -1/2, which tells us that\[\large\rm -\sin(150)=\sin(-150)\]

Answer 4

So which property does it look like?
Odd or even?

Answer 5

even

Answer 6

Ok let's make sure.
If the sine function is our f,
Then we have -f(150) = f(-150)

We could call this 150 our x to simplify it further,
-f(x) = f(-x)

Answer 7

ok

Answer 8

It's not even

Answer 9

`odd functions have this property: f(-x) = -f(x)`

that's what we ended up with, right?

Answer 10

yes