Odpowiedź:
a)
sinα = 1/4
sin²α =(1/4)² = 1/16
1 - cos²α = 1/16
cos²α = 1 - 1/16 = 16/16 - 1/16 = 15/16
cosα = √(15/16) = √15/4
tgα = sinα/cosα = 1/4 : √15/4 = 1/4 * 4/√15 = 1/√15 = √15/15
ctgα = 1/tgα = 15/√15 = 15√15/15 = √15
b)
cosα = 5/13
cos²α = (5/13)² = 25/169
1 - sin²α = 25/169
sinα² = 1 - 25/169 = 169/169 - 25/169 = 144/169
sinα = √(144/169) = 12/13
tgα = sinα/cosα = 12/13 : 5/13 = 12/13 * 13/5 = 12/5 = 2 2/5 = 2,4
ctgα = 1/tgα = 5/12
c)
sinα = 8/9
sin²α = (8/9)² = 64/81
1 - cos²α = 64/81
cosα² = 1 - 64/81 = 81/81 - 64/81 = 17/81
cosα = √(17/81) = √17/9
tgα = sinα/cosα = 8/9 : √17/9 = 8/9 * 9/√17 = 8/√17 = 8√17/17
ctgα = 1/tgα = 17/8√17 = 17√17/(8 * 17) = √17/8
