Find the exact value of the expression

The answer to your question is the letter C

Step-by-step explanation:

Data

sec Ф = 9/2

tan Ф = ?

To solve this problem use trigonometric functions.

1.- The first condition is that the angle must be in the fourth quadrangle

(270° < Ф < 360°).

2.- Write the trigonometric function sec.

           sec Ф = hypotenuse / adjacent side   and sec Ф = 9/2

then, hypotenuse = 9   adjacent side = 2

3.- Use the Pythagorean theorem to find the adjacent side.

           Hypotenuse² = Opposite side² + Adjacent side²

-Solve for Opposite side

            Opposite side² = Hypotenuse² - Adjacent side sie²

-Substitution

            Opposite side² = 9² - 2²

-Simplification

            Opposite side² = 81 - 4

            Opposite side² = 77

            Opposite side = √77

4.- Find the tan Ф

             tan Ф = Opposite side/Adjacent side

-Substitution

             tanФ = -√77 / 2    It is negative because in the fourth quadrangle

                                           tan is negative.

i pretty sure it is