Find the exact value of csc ø, if cos ø= 1/9; 180° less ø less than 270°

The answer to your question is: the first option  - 9/

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 =    b = opposite side

But b is negative because we are in the third quadrant.

          b = -

Finally   csc Ф = hypotenuse / opposite side

             csc Ф = - 9 /

the graph in the attached figure

step-by-step explanation:

we have

using a graphing tool

the graph in the attached figure

the roots are ( x-intercepts) x=-0.5,x=1,x=3

the y-intercept is the point (0,3)