solve cos(-.72); 180 < theta < 270

Question

this problem by all accounts seems unsolvable. because you get 136 and and that isn't in between 180 and 270. What am I doing wrong??

Answer 1

The cosine inverse function is defined over the range for angles from 0 to 180 degrees.  If the cosines are positive, then angles are in the first quadrant.  If the cosines are negative, then the angles are in the second quadrant.

 

BUT you can take the answer (136.054^o) and recognize that there's an angle in the THIRD quadrant having the same cosine!  For 136.054^o, the REFERENCE ANGLE is 43.946^o.

 

The angle 180 + 43.946 degrees is what you want...its cosine is -0.72, and it's in quadrant three.