Odpowiedź:
zad 1
sinα = 6/10 = 3/5
cosα = 8/10 = 4/5
tgα = 6/8 = 3/4
ctgα = 8/6 = 4/3 = 1 1/3
zad 2
c = √(12² + 6²) = √(144 + 36) = √180 = √(36 * 5) = 6√5
sinα = 6/6√5 = 1/√5 = √5/5 sinβ = 12/6√5 = 2/√5 = 2√5/5
cosα = 12/6√5 = 2/√5 = 2√5/5 cosβ = 6/6√5 = 1/√5 = √5/5
tgα = 6/12 = 1/2 tgβ = 12/6 = 2
ctgα = 12/6 = 2 ctgβ = 6/12 = 1/2
zad 3
a) tg30° * sin60° = √3/3 * √3/2 = (√3)²/6 = 3/6 = 1/3
b) sin²30° + cos²45° = (1/2)² + (√2/2)² = 1/4 + 2/4 = 3/4
c) ctg30° * (cos60° - tg60°) = √3 * ( 1/2 - √3) = √3/2 - 3 = (√3 - 6)/2
