czy w podpunkcie a)jest tgα=2,4? jeżeli tak to: tgα=2,4 tgα=sinα/cosα oraz sin²α+cos²α=1 sinα/cosα=2,4 2,4=12/5 sinα=12/5 *cosα (12/5 *cosα)²+cos²α=1 144/25 *cos²α+cos²α=1 169/25* cos²α=1/:169/25 cos²α= 25/169 cosα = 5/13 lub cosα = -5/13 sinα = 12/5 × 5 / 13 lub sinα=12/5 ×(-5/13) sin=12/13 sinα = -12/13 ctgα=1/tgα ctgα = 5/12 b)tgα=3/2 tgα=sinα/cosα oraz sin²α+cos²α=1 sinα/cosα=3/2 sinα=3/2 *cosα (3/2 *cosα)²+cos²α=1 9/4 *cos²α+cos²α=1 13/4 * cos²α=1/:13/4 cos²α= 4/13 cosα = 2/√13 lub cosα = -2/√13 cosα= 2√13/13 cosα= -2√13/13 sinα = 3/2 × 2√13/13 lub sinα=12/5 ×(-2√13/13) sin=3√13/13 sinα = -3√13/13 ctgα=1/tgα ctgα = 2/3 c)ctgα=√2 tgα=1/ctgα tgα = 1/√2 tgα=√2/2 ctgα=cosα /sinα cosα/sinα= √2 cosα=√2*sinα sin²α+cos²α=1 sin²α+cos₂α=1 sin²α+(√2*sinα)²=1 sin²α+2sin²α=1 3sin²α=1/:3 sin²α=1/3 sinα=1/√3 lub sinα=-1/√3 sinα= √3/3 sinα= √-3/3 cosα=√2 × √3/3 lub cosα=√2 ×(-√3/3) cos=√6/3 cos=-√6/3
