Final answer:
The trigonometric function equal to cos(x)/sin(x) is cot(x).
Step-by-step explanation:
The trigonometric function equal to cos(x)/sin(x) is cot(x).
To understand this, let's recall the definitions of the trigonometric functions in a right triangle. The cosine function is defined as the ratio of the adjacent side to the hypotenuse, cos(x) = Ax/A, and the sine function is defined as the ratio of the opposite side to the hypotenuse, sin(x) = Ay/A.
Dividing cos(x) by sin(x), we get (Ax/A)/(Ay/A) which simplifies to Ax/Ay. This is the definition of cot(x), which stands for the cotangent function.
The trigonometric function equal to cos(x)/sin(x) is known as the cotangent, which is commonly written as cot(x). This relationship comes from rearranging the definition of the basic trigonometric functions. Specifically, cotangent is the reciprocal of tangent, which is defined as sin(x)/cos(x).
This means that cot(x) = cos(x)/sin(x), providing the answer to the student's question.