the second-to-last hint he gives tells you the desired value, but not how it is actually got
There are only four hints, not five. I'm guessing that you're referring to the last hint. (The fifth line is the answer.)
In the last hint, Khan is not telling you the desired value. Rather, he simply states an appropriate conclusion, based on his line of reasoning above that. It is this conclusion which makes the answer obvious.
Perhaps, your uncertainly results from a lack of understanding regarding inverse trig functions OR unfamiliarity with the tangent function. I'm not sure.
The first hint assigns a symbol to represent the unknown angle that you've been asked to find. (Khan assigns the symbol θ.)
The second hint shows what the given information
means; that is, what it means to say that angle θ equals the inverse tangent of zero. (This comes directly from the definition of inverse trig functions.)
The third hint states explicitly that angles coming out of the inverse tangent function must lie within the known range of that function.
The fourth hint states an obvious conclusion: there is only
one angle within this range whose tangent is zero. If this is not obvious to you, then you must not be considering either of the following two facts.
(1) Within the restricted domain of [-90°,90°], the graph of the tangent function goes through the origin, AND the origin is the only place where tangent equals zero (in that vicinity).
or
(2) tan(θ) = sin(θ)/cos(θ) --
and the only way that sin(θ)/cos(θ) can equal zero is if sin(θ) = 0 AND cos(θ) ≠ 0. Where does that happen, within the restricted domain of [-90°,90°]?
If you're still stuck on this exercise, please continue by asking specific questions or explain what you're thinking. Cheers :cool:
