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.

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.