<prompt> Miongoni mwa pembetatu zote ABC, pata thamani ya juu zaidi ya sin A sin B sin C.  <response>: Tunaweza kuandikaanzaalignsin B sin C frac12 cos B - C - cos B C frac12 cos B - C - cos 180circ - A frac12 cos B - C cos A.mwishoalignKishaanzaalignsin A dhambi B sin C sin A frac12 cos A frac12 cos B - C fracsqrt52 kushoto frac2sqrt5 sin A frac1sqrt5 cos A kulia frac12 cos B - C fracsqrt52 kushoto cos theta sin A sin theta cos A kulia frac12 cos B - C fracsqrt52 sin A theta frac12 cos B - C,endalignambapo theta ni pembe kali kiasi kwamba cos theta frac2sqrt5 na sin theta frac1 sqrt5.Kishafracsqrt52 sin A theta frac12 cos B - C le fracsqrt5 2 frac12 frac1 sqrt52. Usawa hutokea wakati A fracpi2 - theta na B C fracpi - A2, kwa hivyo thamani ya juu ni frac1 sqrt52. 