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Carolzzinha22
@Carolzzinha22
August 2019
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A soma das raizes da equação sen2x + 2cos2(x) = 7/4, para 0 <igual x < 2pi é:
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Comentários (3)
Se for sen²(x) + 2 * cos²(x) =7/4
sen²(x) + cos²(x) + cos²(x)=7/4
***sen²(x)+cos²(x)=1
1+cos²(x)=7/4
cos²(x) =7/4-1
cos²(x)=3/4
cos (x) =-
√3/2 ==>x=π-π/6=5π/6 , x=π+π/6 =7π/6
ou
cos (x) =√3/2 ==>x=π/6 , x =2π-π/6=11π/6
Resposta: {π/6 , 5π/6 , 7π/6 , 11π
/6}
Ele queria a soma:
soma =
π/6 +5π/6 +7π/6 +11π/6 = 24π/6 = 4
π é resposta pedida
2 votes
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Carolzzinha22
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Carolzzinha22
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Lista de comentários
sen²(x) + cos²(x) + cos²(x)=7/4
***sen²(x)+cos²(x)=1
1+cos²(x)=7/4
cos²(x) =7/4-1
cos²(x)=3/4
cos (x) =-√3/2 ==>x=π-π/6=5π/6 , x=π+π/6 =7π/6
ou
cos (x) =√3/2 ==>x=π/6 , x =2π-π/6=11π/6
Resposta: {π/6 , 5π/6 , 7π/6 , 11π/6}
Ele queria a soma:
soma =π/6 +5π/6 +7π/6 +11π/6 = 24π/6 = 4π é resposta pedida