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Solve for x in the following:​

Solve for x in the following:​-example-1
User Elvikingo
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1 Answer

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Answer:


\boxed{\boxed{ \red{\: x = \begin{cases} (\pi)/(8) + 7 + (k\pi)/(2) \\ - 6 + (\pi)/(12) + (k\pi)/(3) \end{cases}}}}

Explanation:

to understand this

you need to know about:

  • trigonometry equation
  • PEMDAS

tips and formulas:


  • \cos(t) = \sin( (\pi)/(2) - t )

  • \sin(t) - \sin(s) = 2 \cos( (t + s)/(2) ) \sin( (t - s)/(2) )

let's solve:


  1. \sf use \: first \: formula : \\ \sin(5x + 4) = \sin( (\pi)/(2) - (5 x + 4) )\\ \sin(5x + 4) = \sin( (\pi)/(2) - 5 x - 4) \\

  2. \sf move \: the \: expresson \: to \: left \: side \: and \: change \: the \: sign : \\ \sin(5x + 4) - \sin( (\pi)/(2) - 5 x - 4) = 0\\

  3. \sf use \: 2nd \: formula : \\ 2 \cos( (8x - 56 + \pi)/(4) ) \sin( (12x + 72 - \pi)/(4) ) = 0

  4. \sf divide \: both \: sides \: by \: 2 : \\ \cos( (8x - 56 + \pi)/(4) ) \sin( (12x + 72 - \pi)/(4) ) = 0

  5. \sf separate \: the \: equation: \\ \cos( (8x - 56 + \pi)/(4) ) = 0 \\ \sin( (12x + 72 - \pi)/(4) ) = 0

therefore


\therefore \: x = \begin{cases} (\pi)/(8) + 7 + (k\pi)/(2) \\ - 6 + (\pi)/(12) + (k\pi)/(3) \end{cases}

User LearnAsWeGo
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