a) fie a - abcisa => A(a,3a) ∈ Gf daca f(a) = 3a
f(a) = 2-3a = 3a/-3a
2-6a=0/-2
-6a=-2
a= 2/6 => a =1/3| => A(1/3, 1)
3a=3*1/3=1 |
b). f(0)= 2-3*0=2 B(0,2)
f(x)= 0 = 2-3x
-3x=-2
x=2/3 C (3/2,0 )
Faci graficul si reprezinti punctele B si C.
sin dintre Gf si Axa abciselor este sin(<Gf, Ox) = Sin(<BCO)= Cateta opusa/ ipotenuza=
=OB/BC = 2/BC
triunghi BOC| (T.P)
m(<O)=90 | => OB² + OC² =BC²
2²+(2/3)²= BC²
BC²= 4+ 4/9
BC²= 36/9 + 4/9
BC²= 40/9
BC =√40/√9
BC = (2√10)/3
sin (<BCO)=2/(2√10/3)= 2* 3/ (2√10) = 6/(2√10) = 3/(√10)(rationalizam) = (3√10)/10.
