Answer: OPTION D.
Step-by-step explanation:
For this exercise it is important to remember the following Trigonometric Functions:
[tex]sin\alpha =\frac{opposite}{hypotenuse}\\\\cos\alpha =\frac{adjacent}{hypotenuse}\\\\tan\alpha =\frac{opposite}{adjacent}\\\\sec\alpha =\frac{hypotenuse}{adjacent}\\\\csc\alpha =\frac{hypotenuse}{opposite}\\\\cot\alpha =\frac{adjacent}{opposite}[/tex]
Knowing this, we can identify that:
[tex]cosA=\frac{AC}{AB}=\frac{x}{AB}\\\\sinB=\frac{AC}{AB}=\frac{x}{AB}\\\\secA=\frac{AB}{AC}=\frac{AB}{x}\\\\tanB=\frac{AC}{BC}=\frac{x}{y}[/tex]
Therefore, the ratio [tex]\frac{x}{y}[/tex] is equivalent to this Trignometric function:
[tex]tanB=\frac{x}{y}[/tex]
