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    x=2cos(theta) + sin (theta)
    y= cos (theta) + 2sin (theta)

    Show that for any point on the curve x^2 + y^2 = 5 + 4sin2(theta).
    I tried squaring both x and y and adding them together but I cant seem to get the right answer.
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    (Original post by Fross877)
    x=2cos(theta) + sin (theta)
    y= cos (theta) + 2sin (theta)

    Show that for any point on the curve x^2 + y^2 = 5 + 4sin2(theta).
    I tried squaring both x and y and adding them together but I cant seem to get the right answer.
    Correct approach.

    Let's see what you've written to determine where you're tripping up.
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    (Original post by RDKGames)
    Correct approach.

    Let's see what you've written to determine where you're tripping up.
    x^2 + y^2 = 5cos^2 (theta) + 3sin^2 (theta)
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    (Original post by Fross877)
    x^2 + y^2 = 5cos^2 (theta) + 3sin^2 (theta)
    OK, that's not much to go on, it is clearly wrong.

    How did you get to this point? Show your working out.
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    (Original post by RDKGames)
    OK, that's not much to go on, it is clearly wrong.

    How did you get to this point? Show your working out.
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    (Original post by Fross877)
    ...
    GCSE type mistake.

    x^2 = (2\cos \theta + \sin \theta)^2 = (2\cos \theta + \sin \theta)(2\cos \theta + \sin \theta)

    Expand the brackets and you'll notice that it is not just 4\cos^2 \theta + \sin^2 \theta
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    (Original post by Fross877)
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    You've squared x and y wrong - remember to multiply each term by each term.

    i.e. (a+b)^2 = a^2 + 2ab + b^2, not just a^2 + b^2
 
 
 
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