Final answer:
In the study of trigonometry, the sine function corresponds to opposite/hypotenuse, cosine matches adjacent/hypotenuse, tangent is opposite/adjacent, cosecant is hypotenuse/opposite, secant is hypotenuse/adjacent, and cotangent is adjacent/opposite.
Step-by-step explanation:
Trigonometric Functions and Right Triangle Definitions
In the context of a right triangle, the trigonometric functions are defined by the following ratios:
Sine (sin) of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. Therefore, the correct match for sine is opposite/hypotenuse.
Cosine (cos) of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. Hence, the match for cosine is adjacent/hypotenuse.
Tangent (tan) is the ratio of the opposite side to the adjacent side. This makes the match for tangent opposite/adjacent.
Cosecant (csc) is the reciprocal of sine, which means its ratio is hypotenuse/opposite.
Secant (sec) is the reciprocal of cosine, which corresponds to hypotenuse/adjacent.
Cotangent (cot) is the reciprocal of tangent, so it is adjacent/opposite.
Therefore, for the questions provided:
Sine (a) corresponds to the ratio opposite/hypotenuse.
Cosine (b) matches the ratio adjacent/hypotenuse.
Tangent (c) is represented by the ratio opposite/adjacent.
Cosecant (d) equates to the ratio hypotenuse/opposite.
Secant (e) equates to the ratio hypotenuse/adjacent.
Cotangent (f) is associated with the ratio adjacent/opposite.
Understanding these trigonometric ratios and how they apply to right triangles is fundamental in the study of trigonometry, a branch of mathematics that deals with the relationships between the sides and angles of triangles.