Question

Sa se precizeze in ce cadran sunt unghiurile cu masurile:

a)π/15

b)3π/4

c)24π/5

d)8π/3

e)111π/2

f)707π/3

g)-11π/3

h)-23π/6

Va roog, urgent!

Answer 1

a) cadran 1
b)cadran 2
c)cadran 2, 20pi+4pi totul pe 5=4pi+4pi pe5, 4pi pe 5 cadran 2
d) 8pi/3 =(6pi+2pi)/3=2pi+2pi/3, 2pi/3 cadran 2
e) 111pi/2=(110pi+pi)/2=55pi+pi/2, pi/2 cadran1
f)707pi/3=(705pi+2pi)/3=235pi+2pi/3, 2pi/3 cadran 2
g)-11pi/3=(-9pi-2p)/3=-3pi-2pi/3,-2pi/3 cadran 2
h)-23pi/6=(-24pi+pi)/6=-4pi+pi/6,pi/6 cadran 1
intregii sunt lungimea cercului de forma 2kpi (perioada) si nu se iau in considerare, se ia doar ce ramane

Answer 2

sa ne amintim
sens trigonometric (pozitiv) =sens INVERS ACELOR DE CEASORNIC  (desfacerea unui surub/robinet normal)

primul cadran 0-90 grade⇔(0; π/2)
cadran II                            (π/2  ;π)   
 III                                     (π;3π/2)
 IV                                     (3π/2;2π)  

pt α>2π, se ia in considerare {α/2π} unde prin {x} am inteles partea fractionara din x

asadar
caz    cadran

a)      I
 b)   II
c) { 24π/5}=4π/5
 π/2=2.5π/5<4π/5<4π/4=π, deci cadran2
altfel ( babeste) 4*180/5=4*36=144 grade, cadran2

d) 8π/3=6π/3+2π/3=2π/3 ⇄120°, cadran2

e) 111π/2= 108π/2 +3π/2=54π+3π/2=3π/2  frontiera intre cadranele III si IV, semidreapta negativa a axei Oy
 


f)707π/3=705π/3+2π/3=235π+2π/3=234π+π+2π/3=π+2π/3⇆(180+120)°=300°, cadran IV


g) -11π/3=-6π/3-5π/3=-5π/3=-6π/3+π/3=-2π+π/3=π/3⇆-300°=+60° cadran 1  vezi atas

h) -23π/6=-24π/6+π/6=-4π+π/6=π/6⇆30°, cadran1