How do you evaluate #tan^-1 (-sqrt3)# without a calculator?
Trig table and unit circle give:
The principal value is
Students are only expected to know two triangles, 30/60/90, and 45/45/90, and be able to figure them out in all four quadrants.
It's a goofy way to structure an entire course, but once you understand it problems become easier.
Rule of thumb,
We know 30 and 60 degrees have sine and cosine
Tangent is slope, sine over cosine, so we have a sine of
The principal value is in the fourth quadrant,