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    Solve for 0 >(or equal) x < 2pi

    Sin 2x = cos 2x

    The mark scheme says tan 2x = 1, now i understand if you divide them both you'd get tan 2x but where does the 1 come from?

    Thanks in advance.
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    If you divide sin2x by cos2x you get tan2x
    but you also have to divide cos2x by cos2x which equals 1.
    ( what you do to one side you must do to the other etc)
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    If you divide through by \cos 2x on both sides of the equation then you end up with \tan 2x on the LHS and 1 on the RHS... since \dfrac{\cos \theta}{\cos \theta} = 1 (except when \theta = \dfrac{(2n-1)\pi}{2}).
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    I'm doing the same question now! :p:

    I'd like to ask, once having done tan2∅=1

    and ∅ = 22.5, 202.5

    Where do the other two solutions come from?

    I will convert back to radians in the end...

    Thank you
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    (Original post by gottastudy)
    I'm doing the same question now! :p:

    I'd like to ask, once having done tan2∅=1

    and ∅ = 22.5, 202.5

    Where do the other two solutions come from?

    I will convert back to radians in the end...

    Thank you
    loool

    I can answer this

    It's 2x therefore you'll have to divide the final answer by 2 at the end.
    So instead of finding the values for 0 to 360 find them to 720, then when you divide them by 2 so you get x not 2x, you'll get the real values.

    Only state the final values within the original range 0 to 360 though.
    Do you understand what i mean?
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    You get 1 by dividing 2 of the same terms. cos2x/cos2x=1 or in any case x/x=1

    ^ Because it's 2theta it's 2 x 360=720 degrees, so you go around again, then divide by 2 to get theta
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    (Original post by gottastudy)
    I'm doing the same question now! :p:

    I'd like to ask, once having done tan2∅=1

    and ∅ = 22.5, 202.5

    Where do the other two solutions come from?

    I will convert back to radians in the end...

    Thank you
    Firstly it's in radians so you should get 1/4pi and 5/4pi then the other 2 would be 2pi + 1/4pi and 3pi + 1/4pi

    which will give 2x = 1/4pi, 5/4pi, 9/4pi, 13/4pi
    x = 1/8pi, 5/8pi, 9/8pi and 13/8pi
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    (Original post by Spongebob*No*Pants)
    loool

    I can answer this

    It's 2x therefore you'll have to divide the final answer by 2 at the end.
    So instead of finding the values for 0 to 360 find them to 720, then when you divide them by 2 so you get x not 2x, you'll get the real values.

    Only state the final values within the original range 0 to 360 though.
    Do you understand what i mean?
    Thank you rep when it resets

    hold on....i think I have it now...

    Is it:

    2∅ = 720



    45 + 360 (whole cycle) = 405 = 2∅
    225 + 360 = 585 = 2∅

    Then divide by 2, to get ∅?
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    (Original post by gottastudy)
    Thank you rep when it resets

    hold on....i think I have it now...

    Is it:

    2∅ = 720



    45 + 360 (whole cycle) = 405 = 2∅
    225 + 360 = 585 = 2∅

    Then divide by 2, to get ∅?
    :yep:
 
 
 
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