Trigonometry - Exact Trigonometric Values and the Unit Circle

It is given that \(\tan A = -\frac{3}{4}\), where \(180^\circ \leq A \leq 360^\circ\).

1. Without using a calculator, find the value of
   1. \(\sin A\),
   2. \(\cos A\).
2. It is also known that \(\cos B = \frac{12}{13}\) and that both \(A\) and \(B\) lie in the same quadrant.
   Without using a calculator, find the value of \(\frac{1}{\cos A} + \frac{1}{\sin B}\).