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MATEMÁTICA

AGRONEGÓCIO - TURMA 2º A. MATEMÁTICA. UNIDADE 5 Conteúdo: Transformações Trigonométricas Duração: 1 0 40’ 22/10/13. Matemática – Sistemas Lineares André Luiz. Exemplos.

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MATEMÁTICA

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  1. AGRONEGÓCIO - TURMA 2º A MATEMÁTICA UNIDADE 5 Conteúdo: Transformações Trigonométricas Duração: 10 40’ 22/10/13 Matemática – Sistemas Lineares André Luiz

  2. Exemplos 01- Calcule o cosx na equação 2cos2x+cosx-1=0 2cos2x+cosx-1=0 ∆=1-4.4.(-3) 2(cos²x-sen²x)+cosx-1=0 ∆=49 2(cos²x-(1-cos²x))+cosx-1=0 Cosx=(-1±7)/2.4 2(2cos²x-1)+cosx-1=0 Cosx’=(-1-7)/8 Cosx’=-1 4cos²x - 2 + cosx-1=0 Cosx”=(-1+7)/8 4cos²x+cosx-3=0 Cosx”=3/4

  3. Exemplos 2- Sabendo que tgx + cotgx = 3, calcule sen 2x tgx + cotgx = 3 senx * cosx =1/3 senx + cosx =3 cosxsenx sen²x + cos²x sen2x= 2senx.cosx =3 senx . cosx sen2x= 2(1/3) 1 =3 sen2x= 2/3 senx . cosx

  4. Exemplos 3 Encontrar os ângulos x e y pertencentes ao intervalo [0,2π] no sistema / / Senx=2-1 Sen(x+y)+sen(x-y)=2 Senx + cosy=2 Senx=1 • x= π/2 senx.cosy+seny.cosx + senx.cosy - seny.cosx=2 senx+cosy =2 senx.cosy =1 (2-cosy).cosy=1 2senx.cosy =2 senx+cosy =2 Senx=2-cosy senx+cosy =2 • y =0 ou y=2π 2cosy - cos²y = 1 cosy =1

  5. Exemplos 4) Calcule tgx, sabendo que cos²x + 3 senx.cosx – sen²x=1 2tg²x – 3tgx=0 Tgx = senx Tgx(2tgx – 3)=0 cosx Tgx=3/2 tgx = 0 ou cos²x + 3 senx.cosx – sen²x= 1 cos²x + 3 senx.cosx – sen²x = 1 Cos²x Cos²x Cos²x Cos²x 1 + 3 tgx - tg²x = sec²x 1 + 3 tgx - tg²x = 1+ tg²x

  6. Exercícios 1) Sendo senx=5/13 e Cosx=12/13 com x sendo um arco do 1º quadrante, determine o valor de tg2x. 2)

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