Ensino Médio ⇒ Trigonometria: Equação Trigonométrica

[Liu12]

Resolva a equação [tex3]\text{sen}\,x + \cos\,x \,-\,1\,=\, 0[/tex3] no intervalo [tex3][0, 2\pi].[/tex3]

[triplebig]

• [tex3]\sqrt{1\,-\,\cos^2\,x}\,=\,1\,-\,\cos\,x[/tex3]
  
  [tex3]1\,-\,\cos^2\,x\,=\,(1\,-\,\cos\,x)^2[/tex3]
  
  [tex3]1\,-\,\cos^2\,x\,=\,1\,+\,\cos^2\,x\,-\,2\,\cos\,x[/tex3]
  
  [tex3]2\,\cos^2\,x\,=\,2\,\cos\,x[/tex3]
  
  [tex3]\cos^2\,x\,-\,\cos\,x\,=\,0[/tex3]
  
  [tex3]\cos\,x(\cos\,x\,-\,1)\,=\,0[/tex3]
  
  [tex3]\begin{cases}\cos x\,=\,0 \\ \cos\,x\,=\,1 \end{cases}[/tex3]
  
  [tex3]S\,=\,\left\{0,\,\Large\frac{\pi}{2}\large ,\,\pi ,\,\Large\frac{3\pi}{2}\large\right\}[/tex3]

[Liu12]

Valeu,colega.
Muito obrigada.