What is #Arctan (-1/3 * sqrt3)#?
We need to remember what the tan is. See the following two right triangles:
These two angles are the same since
Pytagoras says that the hypotenuse squares is the sum of the square of the sides, i.e.
Hopefully you remember that in an equilateral triangle all sides are equal, and that each angle is
This means that
Except that we have been working with positive values, so
There are really very few non-trivial trig function values that student is expected to have at their fingertips. Besides the multiples of
We hopefully can already recognize
Now we learn the tangents.
That's pretty close to the one we need for this problem; let's enumerate the others.
Complementary angles have reciprocal tangents.
OK, we learned to recognize
The general solution to