Question

Based on the figure below, the ratio of x/y is equivalent to which trigonometric function?

Answer 1

Answer: OPTION D.

Step-by-step explanation:

For this exercise it is important to remember the following Trigonometric  Functions:

$sin\alpha =\frac{opposite}{hypotenuse}\\\\cos\alpha =\frac{adjacent}{hypotenuse}\\\\tan\alpha =\frac{opposite}{adjacent}\\\\sec\alpha =\frac{hypotenuse}{adjacent}\\\\csc\alpha =\frac{hypotenuse}{opposite}\\\\cot\alpha =\frac{adjacent}{opposite}$

Knowing this, we can identify that:

$cosA=\frac{AC}{AB}=\frac{x}{AB}\\\\sinB=\frac{AC}{AB}=\frac{x}{AB}\\\\secA=\frac{AB}{AC}=\frac{AB}{x}\\\\tanB=\frac{AC}{BC}=\frac{x}{y}$

Therefore, the ratio $\frac{x}{y}$ is equivalent to this Trignometric function:

$tanB=\frac{x}{y}$