I'm not sure if I'm suppossed to find the value of 5pi/6 (which is 1/2) and then subtract 2pi from it. Or is it sin(5pi/6)-sin(2pi)?

Wow! They were supposed to teach you about functions before diving so deep into trig! To get up to speed, try a lesson on

functions and another on

function notation. Specifically, you'll see that the parentheses in function notation is

**not** the same as parentheses for multiplication!

In this case, you have the function, sine, being taken of the simplified value of -pi/6.

Since the graph is already flexed back downward (in other words, it's not in the middle of its flexing) at (0, -1), then the function isn't going to be tan(something) - 1. It looks to me like you have a phase shift going on, but that's about all.

In f(x) = tan(x), what is the value of tan(-pi/4)? How can you relate that to the graph?