Question

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

A
cos A

B
sin B

C
sec A

D
tan B

Answer 1

Answer: OPTION D.

Explanation:

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

`sin\alpha =(opposite)/(hypotenuse)\\\\cos\alpha =(adjacent)/(hypotenuse)\\\\tan\alpha =(opposite)/(adjacent)\\\\sec\alpha =(hypotenuse)/(adjacent)\\\\csc\alpha =(hypotenuse)/(opposite)\\\\cot\alpha =(adjacent)/(opposite)`

Knowing this, we can identify that:

`cosA=(AC)/(AB)=(x)/(AB)\\\\sinB=(AC)/(AB)=(x)/(AB)\\\\secA=(AB)/(AC)=(AB)/(x)\\\\tanB=(AC)/(BC)=(x)/(y)`

Therefore, the ratio
`(x)/(y)` is equivalent to this Trignometric function:

`tanB=(x)/(y)`