Question

Oblicz długość łuku i pole wycinka:
a) alfa=45° r=4°
b) alfa=120° r=3°
c) alfa=210° r=6°
d) alfa=150° r=5°
e) alfa=270° r=2°

Answer 1

P - pole wycinka = παr²/360°
ł - długość łuku = παr/180°
a)
ł = π * 45° * 4/180° = 4π/4 = π
P = πα4²/180° = π45° * 16/180° = 4π
b)
ł = π * 120° * 3/180° = 2π
P = π * 120° * 3²/360° = π * 120° * 9/360° = 3π
c)
ł = π * 210° * 6/180° = 7π/2 = 3,5π
P = π * 210° * 6²/360° = π * 210° * 36/360 =  21π
d)
ł = π * 150° * 5/180° = 25π/6
P = π * 150° * 5²/360° = π * 150° * 25/360° = 125π/2 = 62,5π
e)
ł = π * 270° * 2/180° = 3π
P = π * 270° * 2²/360° = π * 270° * 4/360° = 3π