Final answer:
The student wants to know about identifying trigonometric ratios in a right-angled triangle. Sine and cosine ratios are related to the sides of the triangle, whereas tangent and cotangent are based on sine and cosine. Option A is correct.
Step-by-step explanation:
Trigonometric ratios are fundamental in understanding relationships in right-angled triangles. The sine and cosine ratios are defined as follows: for a right-angled triangle with angle A, the sine of A (sin A) is the quotient of the triangle's opposite side to angle A (denoted as y) and the hypotenuse (denoted as h).
Conversely, the cosine of A (cos A) is the quotient of the adjacent side to angle A (denoted as x) and the hypotenuse h.
The tangent and cotangent ratios can be derived from sine and cosine; tangent (tan A) is the ratio of sine to cosine, whereas cotangent (cot A) is its reciprocal. The secant and cosecant are the reciprocals of cosine and sine, respectively.
For example, in a right-angled triangle where angle A is known and the lengths of the adjacent (Ax) and the opposite sides (Ay) are known, one can determine the sine and cosine ratios using the formulas: Ay/A = sin A and Ax/A = cos A.
Familiarity with additional trigonometry concepts such as the law of sines and the law of cosines, as well as the sum and difference formulas for sine and cosine (e.g., sin(a ± β) = sin a cos β ± cos a sin β) is integral for solving more complex problems.