resolva as equações seguintes, considerado U = [0,2π[.
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a) Cos x=0
x' =π/2 , x" =3π/2
b) Cos x = √2/2
x'=π/4 , x"=2π -π/4 =7π/4
c) Cos x = 1
x = 2π
d) Cos x= -1/2 ==> Cos-¹ (1/2)=60°=π/3
x'= π -π/3 =2π/2 , x"= π +π/3= 4π/3
e)
3 Cosx +6=0
3cosx = -6
Cos x = -2 (não existe x)
f)
4cos²x = 3
cos²x = 3/4
Cos x = √3/4
Cos x = ± √3/2
{Cos x= +√3/2
x'=π/6 , x"= 2π -π/6=11π/6
{Cos x = -√3/2
x"'= π -π/6=5π/6 , x""= π +π/6=7π/6
x' =π/2 , x" =3π/2
b) Cos x = √2/2
x'=π/4 , x"=2π -π/4 =7π/4
c) Cos x = 1
x = 2π
d) Cos x= -1/2 ==> Cos-¹ (1/2)=60°=π/3
x'= π -π/3 =2π/2 , x"= π +π/3= 4π/3
e)
3 Cosx +6=0
3cosx = -6
Cos x = -2 (não existe x)
f)
4cos²x = 3
cos²x = 3/4
Cos x = √3/4
Cos x = ± √3/2
{Cos x= +√3/2
x'=π/6 , x"= 2π -π/6=11π/6
{Cos x = -√3/2
x"'= π -π/6=5π/6 , x""= π +π/6=7π/6
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