Question

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

Answer 1

The answer to your question is: the first option - 9/
`√(80)`

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 =
`√(80) \\` b = opposite side

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

b = -
`√(80)`

Finally csc Ф = hypotenuse / opposite side

csc Ф = - 9 /
`√(80)`