Answer:
The answer to your question is: the first option - 9/ [tex]\sqrt{80}[/tex]
Step-by-step explanation:
Process
cosФ = adjacent side / hypotenuse
-1/9 = adjacent side / hypotenuse
adjacent side = -1 hypotenuse = 9
c² = a² + b²
b² = c² - a²
b² = 81 - 1
b = [tex]\sqrt{80} \\[/tex] b = opposite side
But b is negative because we are in the third quadrant.
b = -[tex]\sqrt{80}[/tex]
Finally csc Ф = hypotenuse / opposite side
csc Ф = - 9 / [tex]\sqrt{80}[/tex]
