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Math Help - trig question

  1. #1
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    Exclamation trig question

    need help with these questions -

    solve sin(2x-45) = √ 3 / 2

    and

    find general solutions of sin2x=cosx

    thankyou in advance
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  2. #2
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    Re: trig question

    Quote Originally Posted by jshine96 View Post
    need help with these questions -

    solve sin(2x-45) = √ 3 / 2

    and

    find general solutions of sin2x=cosx

    thankyou in advance
    \displaystyle \begin{align*} \sin{(2x - 45)} &= \frac{\sqrt{3}}{2} \\ 2x - 45 &= \left\{ 60, 120 \right\} + 360n , n \in \mathbf{Z} \end{align*}

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    \displaystyle \begin{align*} \sin{2x} &= \cos{x} \\ 2\sin{x}\cos{x} &= \cos{x} \\ 2\sin{x}\cos{x} - \cos{x} &= 0 \\ \cos{x}\left(2\sin{x} - 1\right) &= 0 \\ \cos{x} = 0 \textrm{ or } 2\sin{x} - 1 &= 0 \end{align*}

    Go from here.
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  3. #3
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    Re: trig question

    Quote Originally Posted by jshine96 View Post
    need help with these questions -

    solve sin(2x-45) = √ 3 / 2

    and

    find general solutions of sin2x=cosx

    thankyou in advance
    next time, please post trig questions in the trig forum.
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  4. #4
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    Re: trig question

    sorry, i forgot to add -

    solve sin(2x-45) = √ 3 / 2 for -180 ≤ x ≤ 180
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  5. #5
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    Re: trig question

    Quote Originally Posted by jshine96 View Post
    sorry, i forgot to add -

    solve sin(2x-45) = √ 3 / 2 for -180 ≤ x ≤ 180
    It's solved in exactly the same way, you just let n be whatever values will give you solutions in the given domain.
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  6. #6
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    Re: trig question

    sorry.. i still don't get how to solve it :L [i get the first part]
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  7. #7
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    Re: trig question

    and for this question find general solutions of sin2x=cosx

    i understand what you wrote, but confused on what to do next.. do I solve what x is? like 90, 27, 30, 150?
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