Answer:
d. [tex]1.82\: or\:4.46[/tex]
Step-by-step explanation:
The given trigonometric equation is;
[tex]\sec \theta=-4.0545[/tex]
Recall that;
[tex]\cos \theta=\frac{1}{\sec \theta}[/tex]
[tex]\implies \cos \theta=\frac{1}{-4.0545}[/tex]
[tex]\implies \cos \theta=-0.2466[/tex]
The cosine function is negative in the second and third quadrant.
[tex]\theta=\pi-\cos^{-1}(0.2466)\: or\:\pi+\cos^{-1}(0.2466)[/tex]
[tex]\theta=1.82\: or\:4.46[/tex]
