\( a=\sin 16^{\circ}-\sin 216^{\circ} ; \) \( b=\cos 130^{\circ}-\cos 296^{\circ} ; \) \( c=\operatorname{tg} 140^{\circ}-\operatorname{tg} 220^{\circ} \quad \) sonlarining ishoralarini aniqlang. \( \begin{array}{ll}\text { A) }+;+;+ & \text { B) }+;-;+ \\ \text { C) }-;-;+ & \text { D) }+;-;-\end{array} \)

Keling, ushbu trigonometrik ifodalar so'nggi natijalarini ko'rib chiqaylik! Birinchidan, \( a = \sin 16^{\circ} - \sin 216^{\circ} \) ni hisoblaymiz. \( \sin 216^{\circ} \) nu \( \sin (180^{\circ} + 36^{\circ}) = -\sin 36^{\circ} \) deb bilsak, \( a = \sin 16^{\circ} - (-\sin 36^{\circ}) = \sin 16^{\circ} + \sin 36^{\circ} \) bo'ladi. Bu ifoda musbat bo'ladi, chunki sinus funksiyasi 0 dan katta 36 daraja oralig'idagi qiymatlar. Ikkinchidan, \( b = \cos 130^{\circ} - \cos 296^{\circ} \). Aytish joizki, \( \cos 296^{\circ} = \cos (360^{\circ} - 64^{\circ}) = \cos 64^{\circ} \). Endi \( b = \cos 130^{\circ} - \cos 64^{\circ} \). \( \cos 130^{\circ} \) musbat emas, \( \cos 64^{\circ} \) esa musbat. Buning natijasida \( b < 0 \) bo'ladi. So'nggi hisoblash \( c = \tan 140^{\circ} - \tan 220^{\circ} \) dan iborat. Biz bilamizki, tan funktsiyasi 140 darajadagi musbat, 220 darajadagi esa manfiy. Demak, \( c = + - \) bo'ladi. Natijada, ifodalar ishoralari: \( a: +, b: -, c: + \) Javob: B) \( + ; - ; + \)