If \(\sin x=\frac{5}{13}\) and (x) is in the first quadrant, what is the value of (\tan x)?

Correct answer: \(\frac{5}{12}\)

The direct answer is option C, 5/12. In a right-triangle interpretation, sin x=opposite/hypotenuse=5/13. The Pythagorean relation gives the adjacent side: adjacent²=13²−5²=169−25=144, so adjacent=12. Because x is in the first quadrant, all basic ratios are positive, hence cos x=12/13. Now tan x=opposite/adjacent=5/12, or tan x=sin x/cos x=(5/13)/(12/13)=5/12. Option A, 12/13, is cos x, not tan x. Option B, 13/12, is sec x, the reciprocal of cosine. Option C is correct. Option D, 12/5, is cot x, the reciprocal of tan x. The first-quadrant condition matters because it fixes the positive sign. Memory cue: from the 5-12-13 triangle, sin=5/13, cos=12/13, tan=5/12.