Answer:
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.
