When solving equations for angles between [0, 360] (measured in degrees), remember which quadrants sin and cos are positive and which quadrants they are negative.

First quadrant : sin +
                        cos +

Second quadrant:  sin +
                            cos -

Third quadrant:   sin -
                          cos -

Fourth quadrant:    sin-
                             cos +


Remember when solving equations involving sec and csc, that sec = 1/cos and csc = 1/sin.  Easiest to change back to sin and cos and then finding the angle.