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    I don't really understand the question and how to approach it. I also had trouble with eliminating x or y. This question is supposed to take 5 mins, if someone could take me through their approach to this question I would appreciate it.
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    (Original post by Louisb19)
    https://gyazo.com/509658f8e80ec97536c78a1322acac3b

    I don't really understand the question and how to approach it. I also had trouble with eliminating x or y. This question is supposed to take 5 mins, if someone could take me through their approach to this question I would appreciate it.
    If you convert those simultaneous equations into matrix form then you have a rotation matrix for  \theta anticlockwise about the origin. There are two ways to view this, the simplest is that the determinant is always 1 so there exists an inverse matrix for all values of theta (though since the trig functions have period 2 \pi this is equivalent to  0 \leq \theta  < 2 \pi ). So for all theta the equations have a unique solution.

    Alternatively rotations are bijective. There must be a point mapping onto (2, 1) whatever  \theta is.

    Disclaimer: No idea if this is right.
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    (Original post by 16Characters....)
    If you convert those simultaneous equations into matrix form then you have a rotation matrix for  \theta anticlockwise about the origin. There are two ways to view this, the simplest is that the determinant is always 1 so there exists an inverse matrix for all values of theta (though since the trig functions have period 2 \pi this is equivalent to  0 \leq \theta  < 2 \pi ). So for all theta the equations have a unique solution.

    Alternatively rotations are bijective. There must be a point mapping onto (2, 1) whatever  \theta is.

    Disclaimer: No idea if this is right.
    I haven't read through this properly but it is not really suitable of the MAT. The best way to do this question is let sin(theta)=s and cos(theta)=c and treat like a usual simultaneous equation
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    (Original post by Gome44)
    I haven't read through this properly but it is not really suitable of the MAT. The best way to do this question is let sin(theta)=s and cos(theta)=c and treat like a usual simultaneous equation
    I tried doing that however I don't really understand what the 4 choices even mean.

    I got something like 2c - s = x and something similar when eliminating y.

    I don't get how this answers helps me towards making a choice.
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    (Original post by Louisb19)
    I tried doing that however I don't really understand what the 4 choices even mean.

    I got something like 2c - s = x and something similar when eliminating y.

    I don't get how this answers helps me towards making a choice.
    for every value of theta you get a unique value of x and y that solves the equations
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    (Original post by Gome44)
    for every value of theta you get a unique value of x and y that solves the equations
    Would it ever make sense that there could not be a value of theta which was invalid.

    If the equation you formed was something like x = c/s could you say that there would be 1 value of theta ( theta = 0 ) in the interval which would not be valid?
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    (Original post by Louisb19)
    Would it ever make sense that there could not be a value of theta which was invalid.

    If the equation you formed was something like x = c/s could you say that there would be 1 value of theta ( theta = 0 ) in the interval which would not be valid?
    yes
 
 
 
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