Principal solution for positive and negative Cot, Sec and Cosec theta values

Dear experts,

In the attached image I have the Principal solution for positive and negative sin theta. The image shows how the negative theta values are reflected as positive alpha values.

Can someone please guide me to an article in public domain for equivalent workings of Cot, cosecant and secant theta.

Thank you
Principal-Solution-for-pos-and-neg-S.pdf