Question

Sa se calculeze:
arctg (1/radical din x), daca x apartine {1/3 ; 1,3}

Answer 1

arctgx:R->(-π/2;π/2)
x=1/3
1/x=3
1/√x=√3
arctg (√3)=π/3

x=1,3
arctg(1/√1,3)= habar n-am, nu e o valoare uzual pt arctg
poate al doilea numar sa fi fost 3, nu 1,3
caz in care 1/x=1/3 si 1/√x=1/√3
caz in care
arctg(1/√3)=π/6


saaau d fapt valorilelui x erau
{1/3 ; 1;3} iar tu intre 1 si 3 ai pus virgula  in locde punct si virgula

si pt x=1
arctg (1/√1)=arctg1=π/4

Answer 2

$\it x\in \left\{\dfrac{1}{3},\ 1,\ 3\right\},\ \ \ arctg\dfrac{1}{\sqrt x} = ?$

$\it I) \ \ x=\dfrac{1}{3} \Rightarrow arctg\dfrac{1}{\sqrt{\dfrac{1}{3}}} = arctg \dfrac{1}{\dfrac{1}{\sqrt3}} = arctg\sqrt3 = 60^0$

[tex]\it II)\ \ x = 1 \Rightarrow arctg\dfrac{1}{\sqrt1} = \dfrac{1}{1} = arctg1= 45^0 \\ \\ \\ III)\ x = 3 \Rightarrow arctg\dfrac{1}{\sqrt3} = arctg \dfrac{\sqrt3}{3} = 30^0 [/tex]