Question

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

Answer 1

Answer:

The answer to your question is: the first option  - 9/ $\sqrt{80}$

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 = $\sqrt{80}$    b = opposite side

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

          b = -$\sqrt{80}$

Finally   csc Ф = hypotenuse / opposite side

             csc Ф = - 9 / $\sqrt{80}$