Mathematical and Physical Journal
for High Schools
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Problem C. 849. (March 2006)

C. 849. Evaluate cot x, given that cot x=sin x?

(5 pont)

Deadline expired on April 18, 2006.


Sorry, the solution is available only in Hungarian. Google translation

Megoldás:

{\cos x\over\sin x}=\sin x,

cos x=sin2x,

cos2x=1-sin2x=1-cos x,

cos2x+cos x-1=0,

\cos x={-1\pm\sqrt{5}\over2},

amiből csak a nagyobbik gyök jó. Innen \sin x=\pm\sqrt{\sqrt5-1\over2}, ennyi ctg x értéke is.


Statistics:

270 students sent a solution.
5 points:96 students.
4 points:97 students.
3 points:50 students.
2 points:11 students.
1 point:6 students.
0 point:6 students.
Unfair, not evaluated:4 solutions.

Problems in Mathematics of KöMaL, March 2006