Odpowiedź:
zad 5
sinα + cosα = 6/5
(sinα + cosα)² = (6/5)² =36/25
sin²α + 2sinαcosα + cos²α = 36/25
sin²α + cos²α + 2sinαcosα = 36/25
1 + 2sinαcosα = 36/25
2sinαcosα = 36/25 - 1 = 36/25 - 25/25 = 11/25
sinαcosα = 11/25 : 2 = 11/25 * 1/2 = 11/50
zad 6
tgα - ctgα = 5/6
(tgα - ctgα)² = (5/6)² = 25/36
tg²α - 2tgαctgα + ctg²α) = 25/36
tgα * ctgα = 1
tg²α + ctg²α - 2 * 1 = 25/36
tg²α + ctg²α = 25/36 - 2 = 25/36 - 1 36/36 = - 1 11/36
zad 6
P = ( - 5 , 12 ) : xp = - 5 , yp = 12
Obliczamy promień wodzący dla punktu P
r = √[(- 5)² + 12²] = √(25 + 144) = √169 = 13
sinα = yp/r = 12/13
cosα = xp/r = - 5/13
tgα = sinα/cosα = 12/13 : (-5/13) = 12/13 * (-13/5)= - 12/5 = - 2 2/5 = - 1,4
ctgα =1/tgα = - 5/12
