Patrick B. answered • 02/19/19
Math and computer tutor/teacher
Use the mnemonic device to help you remember where the trig functions are positive:
"All students take calculus or Add sugar to coffee"
Tangent is negative in quadrants 2 and 4.
inverse tangent of (-0.5) = -26.565051177077989351572....
The angles are 153.4349822922010648428.... and 333.43498822922010648428....
Negating these angles:
206.5650177077989321572.... and 26.565051177077989351572...
The tangent of them is 1/2, both of them!
This makes sense, and here's why:
the first angle is in the second quadrant which means it is between 90 and 180.
Subtracting it FROM 360 puts the angle between 180 and 270, which is the third quadrant,
where the tangent is positive.
Likewise, for the second angle in quadrant 4, between 270 and 360, negating it puts
it between 0 and 90, or quadrant #1, where ALL 3 TRIG function are positive.
