ANSWER
The domain of the function is
or
[-3,6]
EXPLANATION
The domain of a function refers to the values of x for which the function is defined.
From the graph, we can see that the function begins at (-3,6) and ends at (6,-4).
Therefore the function is defined for x=-3 to x=6.
Hence the domain of the function is
or
[-3,6]
Okay, notice one thing right off the bat? 60 degrees on a right triangle (unit circle w/ terminal arm) will create the infamous 30-60-90 triangle.
We can use this to our advantage. Since sin is the y-coordinate on the unit circle. We need to solve for the longest side of a 30-60-90 triangle.
We find that the long side (y) of our 30-60-90 triangle is sqrt(3)/2. Since this is in quadrant 1, we know it is positive.
So -- sin60° = sqrt(3)/2
