Question

Daca x este masura unui unghi ascutit si
tg x=3/4,calculati 3sin x+5 cos x
Va rog
Urgeeent

Answer 1

3sin x+5 cos x /(:cosx)- impartim totul prin cos x pt ca tg x=$\frac{sin x}{cos x}$
3*$\frac{sinx}{cosx} +5* \frac{cosx}{cosx} =3*tgx+5=3* \frac{3}{4} +5= \frac{9}{4} + \frac{20}{4} = \frac{29}{4}$

Answer 2

sin x/cosx=3/4
sin²x/cos²x=9/16
sin²x/(cos²x+sin²x)=9/(16+9)
sin²x=9/25, sinx=+-√9/25, unghiul fiind ascutit sinx>0, sin x=3/5
cosx²x=1-sin²x=1-9/25=16/25, cosx>0, cosx=4/5
3sinx+5cosx=3x3/5+5x4/5=9/5+4=29/5