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jpjones

  • 2 years ago

solve the following equation for x where 0<or = to x<2pi, sin2x=cosx

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  1. Mimi_x3
    • 2 years ago
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    hint: \(sin2x = 2sinxcosx\)

  2. jpjones
    • 2 years ago
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    yes and

  3. Mimi_x3
    • 2 years ago
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    well where are you stuck or show me what you did

  4. jpjones
    • 2 years ago
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    the equation is not solved

  5. Mimi_x3
    • 2 years ago
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    \[ 2sinxcosx = cosx => 2sinxcosx - cosx = 0 \] why dont you try and solve it

  6. sami-21
    • 2 years ago
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    take cos(x) you will have \[\Large \cos(x)[2\sin(x)-1]=0\] now you have two equations \[\Large \implies \cos(x)=0\] \[\Large \implies 2\sin(x)-1=0\] solve these two equations.

  7. jpjones
    • 2 years ago
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    if i knew how to solve these equations i wouldn;t be asking for help

  8. jpjones
    • 2 years ago
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    to this stage i know, but how to solve from here?

  9. Mimi_x3
    • 2 years ago
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    \[\cos(x) = 0 => cosx = \cos\left(\frac{\pi}{2}\right) => x = \frac{\pi}{2} +n*2\pi , n \epsilon\mathbb{Z} \] \[sinx = \sin\left(\frac{\pi}{6}\right) => x = \left(-1\right)^{n}*\frac{\pi}{6} +n*\pi , n \epsilon\mathbb{Z} \]

  10. jpjones
    • 2 years ago
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    i've been to wolfram alpha to mimi

  11. Mimi_x3
    • 2 years ago
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    lol i didnt use wolfram..

  12. jpjones
    • 2 years ago
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    the answer is correct though but i have to show it using the unit circle, or the graph

  13. jpjones
    • 2 years ago
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    i think using the sin wave

  14. Mimi_x3
    • 2 years ago
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    |dw:1345619287591:dw|

  15. sami-21
    • 2 years ago
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    ok let me give you an example then if you have 2cos(x)+1=0 then \[\Large \implies \cos(x)=\frac{-1}{2}\] \[\Large x=\cos^{-1}(\frac{-1}{2})\] there are only two points in 9o.2pi) for which cos(x) is -1/2 they are \[\Large x=\frac{2 \pi}{3}\] \[\Large x=\frac{4 \pi}{3}\] now solve the 2sin(x)-1=0 its quite similar to this.

  16. Mimi_x3
    • 2 years ago
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    for sinx |dw:1345619404355:dw|

  17. sami-21
    • 2 years ago
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    you use wolfram,thats why you are unable to solve these equations by yourself. this wolfram thingy has ruined the students :(. i think at this level students should avoid using that.

  18. Mimi_x3
    • 2 years ago
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    yeah i agree. you should only use it to check your answers

  19. jpjones
    • 2 years ago
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    no i dont use it but i am aware of it

  20. jpjones
    • 2 years ago
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    mimi you've been great i think i should become a fan

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