SOLUTION: tan(45-theta)=-1 , in the interval 0 ≤x<360 -->solve. What I did: 1. tan inverse which gave -45 degrees 2. Using cast diagram -- any clockwise towards the tan and all secti

You are given   = -1.


From it, you conclude that  

    45° -  = 135°       (a)

or

    45° -  = 315°       (b)



From (a),  you have   = 45° - 135° = -90°,  which geometrically is the same as  270°.


From (b),  you have   = 45° - 315° = -270°,  which geometrically is the same as  90°.


So, you conclude that the problem has two solutions:   = 90°  or   = 270°.    ANSWER