trig function of the rest from sec(delta) = -6/5 tan(delta)>0

$$\\sec(\delta) = -6/5 tan(\delta)\\\\\\ \frac{1}{cos(\delta)}}=\frac{-6Sin(\delta)}{5cos(\delta)}\\\\ so\qquad \delta \ne n\pi\;\;radians \quad n\in Z\qquad and\\\\ 1=\frac{-6Sin(\delta)}{5}\\\\ \frac{5}{-6}=sin(\delta)\\\\ \delta $must be in 3rd or 4th quadrant$\\ $but tan has to be neg so $\delta $ must be in the 4th quad $\\\\ \delta=asin(\frac{-5}{6})$$

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}^{\!\!\mathtt{-1}}{\left({\mathtt{\,-\,}}{\frac{{\mathtt{5}}}{{\mathtt{6}}}}\right)} = -{\mathtt{56.442\: \!690\: \!238\: \!079^{\circ}}}$$

$$\delta \approx -56^0\pm 360N\qquad where \quad N\in Z$$