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    For a question that says solve for \theta between the interval 0 and 360.

     Cos^2 \frac{\theta}{2} = 1 + Sin\frac{\theta}{2}


    Can I start by multiplying by 2? As this will lead me to a different answer (from what I've tried unless I did it wrong) or do I just have to factorise keeping the \frac{\theta}{2} in there?

    Thanks!
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    (Original post by Secret.)
    For a question that says solve for \theta between the interval 0 and 360.

     Cos^2 \frac{\theta}{2} = 1 + Sin\frac{\theta}{2}


    Can I start by multiplying by 2? As this will lead me to a different answer (from what I've tried unless I did it wrong) or do I just have to factorise keeping the \frac{\theta}{2} in there?

    Thanks!
    I'd start by writing cos2 as 1 - sin2
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    (Original post by Secret.)
    For a question that says solve for \theta between the interval 0 and 360.

     Cos^2 \frac{\theta}{2} = 1 + Sin\frac{\theta}{2}


    Can I start by multiplying by 2?
    Why would you multiply by 2

    That would just give you 2\cos ^2\frac{\theta}{2} = 2 + 2\sin \frac{\theta}{2}
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    (Original post by TenOfThem)
    Why would you multiply by 2

    That would just give you 2\cos ^2\frac{\theta}{2} = 2 + 2\sin \frac{\theta}{2}

    Ah okay thanks! I thought the x2 would get rid of the 2 in  \frac{\theta}{2} thanks for clearing that up
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    make cos^2x= 1-sin^2x (x replaces 1/2 theta)

    you get sin^2x+sinx=0

    sinx(sinx+1)=0

    you get sin(1/2 theta)= 0,-1 then just multiply your answers by two and use the ones that fit in the interval.

    Once again I think i might be wrong but lets hope im not lol
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    Quick question please:

    for  Cos^2 \frac{\theta}{2} = 1 + Sin\frac{\theta}{2}

    I get the answers:
    0, 180 and 360
    -90 and 270

    Now as the range in the question said  0 \leq x \geq 180

    I cancel of the 360 in the top, however I was taught that you 'wind back a cycle' of 180 from answers outside the range, would the 360 not be within range?
    Or does the answers have to be within range as when they are  \frac{\theta}{2}
    I understand that the -90 would be cancelled but if I am supposed to wind back a cycle of 180 for 360 and 270 wouldn't they be within range?


    I hope that makes sense and thanks!
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    (Original post by Secret.)
    Quick question please:

    for  Cos^2 \frac{\theta}{2} = 1 + Sin\frac{\theta}{2}

    I get the answers:
    0, 180 and 360
    -90 and 270

    Now as the range in the question said  0 \leq x \geq 180

    I cancel of the 360 in the top, however I was taught that you 'wind back a cycle' of 180 from answers outside the range, would the 360 not be within range?
    Or does the answers have to be within range as when they are  \frac{\theta}{2}
    I understand that the -90 would be cancelled but if I am supposed to wind back a cycle of 180 for 360 and 270 wouldn't they be within range?


    I hope that makes sense and thanks!
    If

    \theta = 0, 360, 720, -180, 540

    and

     0 \leq \theta \leq 360

    then you have 2 solutions.
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    (Original post by Secret.)
    Ah okay thanks! I thought the x2 would get rid of the 2 in  \frac{\theta}{2} thanks for clearing that up
    Nope, because cos() and sin() are functions. If you multiply, you just get a multiple of that function.

    If you still need convincing, just consider some simple function such as:

    f(x) = x + 2


    You need to solve for the whole parameter passed to the function before you can fiddle with it to end up with just a part of it.

    i.e. in this case, solve for theta/2, then multiply to find theta, as other's have explained.
 
 
 
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