^{2} - do kwadratu 1. Pole równoległoboku = 2 Pola trójkątów Pole trójkąta = a * b * 1/2 * sinα P równoległoboku = 2 * 1/2 * 3 * 7 * sin56° = 21 * 0.829 = 17,409 cm2 ~ 17,4 cm2 2. a) (sinα + cosα)^{2} + (sinα - cosα)^{2} = 2 L = (sinα + cosα)^{2} + (sinα - cosα)^{2} L = sin^{2}α + 2sinα*cosα + cos^{2}α + sin^{2}α - 2sinα*cosα + cos^{2}α L = sin^{2}α + 2sinα*cosα + cos^{2}α + sin^{2}α - 2sinα*cosα + cos^{2}α L = sin^{2}α + cos^{2}αsin^{2}α + cos^{2}α + sin^{2}α + cos^{2}α L = 2(sin^{2}α + cos^{2}α) L = 2 * 1 L = 2 L = P To jest tożsamość. 3. cosα = 5∕13 cosα = x/13 x = 5 sinα = ? tgα = ? ctgα = ? sin^{2}α + cos^{2}α = 1 sin^{2}α + (5/13)^{2} = 1 sin^{2}α + 25/169 = 1 sin^{2}α = 1 - 25/169 sin^{2}α = 144/169 sinα = 12/13 v sinα = - 12/13 tgα = sinα/cosα tgα = 12/13 / 5/13 v tgα= - 12/13 / 5/13 tgα = 12/5 v tgα= - 12/5 ctgα = 5/12 v ctgα = - 5/12 sinα = 12/13 | | sinα = - 12/13 cosα = 5∕13 | | cosα = 5∕13 tgα = 12/5 | lub | tgα= - 12/5 ctgα = 5/12 | |ctgα = - 5/12
