Lrcalhoun41 Lrcalhoun41
  • 11-11-2018
  • Mathematics
contestada

1 + 5sin^2x= 7sin^2x solve trig equation. Can you show me how to solve this trig equation?

Respuesta :

remotecontrolbrain
remotecontrolbrain remotecontrolbrain
  • 11-11-2018

Answer: [tex]x = \frac{\pi}{4}\pm k\frac{\pi}{2}\,\,\,\,\,\,k=\{0,1,2,...\}[/tex]

Step by step:

[tex]1 + 5\sin^2x= 7\sin^2x\\\sin^2 x\rightarrow z\\1 + 5z = 7z\\2z = 1\\z = \frac{1}{2}\implies \sin^2 x = \frac{1}{2}\\|\sin x| = \frac{1}{\sqrt{2}}\\\sin x = \pm\frac{1}{\sqrt{2}}=\pm\frac{\sqrt{2}}{2}\\\implies x = \frac{\pi}{4}\pm k\frac{\pi}{2}\,\,\,\,\,\,k=\{0,1,2,...\}[/tex]

(Used a table of common angles)

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