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c2 trig identities

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    Hi
    Find the x-coordinates of the points where the curve y = 2 sin x intersects the curve y = 2 − 3cos2 x, for values of x such that −180º ≤ x ≤ 180º.

    so i know that 2sinx=2=2-3cos^2 x
    so far ive done:

    2(1-cosx)=2-3cos^2 x
    2-2cosx=2-3cos^2 x
    3cos^2 x-2cosx = 0
    cosx(3cosx-2)=0

    cosx=2/3 and cosx=0?

    But checked the mark scheme and they've gone the other way where they made everything into sinx. I know how to do this way but why do they not allow cosx?How do I know which one to change it into?
  2. Offline

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    was that
    2sinx=2-3cos^2x ?
    You need to use the identity:
    cos^2 x + sin^2 x =1
    so cos^2 x=1-sin^2 x
    so that
    2-3(1-sin^2 x) -2sinx=0
    2 -3 + 3sin^2x -2sinx=0
    3sin^2x -2sinx -1=0
    then put into a quadratic and solve to find sinx=whatever.
    Sorry if i made any little mistakes in double negatives or whatever
  3. Offline

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    (Original post by sach21sk)
    Hi
    Find the x-coordinates of the points where the curve y = 2 sin x intersects the curve y = 2 − 3cos2 x, for values of x such that −180º ≤ x ≤ 180º.

    so i know that 2sinx=2=2-3cos^2 x
    so far ive done:

    2(1-cosx)=2-3cos^2 x
    2-2cosx=2-3cos^2 x
    3cos^2 x-2cosx = 0
    cosx(3cosx-2)=0

    cosx=2/3 and cosx=0?

    But checked the mark scheme and they've gone the other way where they made everything into sinx. I know how to do this way but why do they not allow cosx?How do I know which one to change it into?
    sinx doesnt equal 1-cosx.

    it is easier if your make sinx the subject
  4. Offline

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    Sorry, that didnt answer the question!
    Because you have cos^2x in the equation, not sin^2x ,you cannot use the trig identity for sin^2x so have to turn the cos^2x into sin.
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    (Original post by DonBorat)
    sinx doesnt equal 1-cosx.

    it is easier if your make sinx the subject
    (Original post by geology.is.gneiss)
    Sorry, that didnt answer the question!
    Because you have cos^2x in the equation, not sin^2x ,you cannot use the trig identity for sin^2x so have to turn the cos^2x into sin.
    does the rule cosx + sinx = 1 not work? or is that not even an identity, i thought it was
  6. Offline

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    (Original post by sach21sk)
    does the rule cosx + sinx = 1 not work?
    No


    Because it is not true
  7. Offline

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    (Original post by sach21sk)
    does the rule cosx + sinx = 1 not work?
    What rule is this ?
  8. Offline

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    (Original post by steve2005)
    What rule is this ?
    nonexistant im afraid:/
    the sin and cos have to be squared...
    OP: at least you know now, and dont mess up in the exam!
  9. Offline

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    (Original post by steve2005)
    What rule is this ?
    nvm, i thought cos^2 x + sin^2 x = 1 had the same rule to that but it doesn't

    (Original post by geology.is.gneiss)
    nonexistant im afraid:/
    the sin and cos have to be squared...
    OP: at least you know now, and dont mess up in the exam!
    lol yeah so glad I found out before tomorrow, thanks
  10. Offline

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    (Original post by sach21sk)
    nvm, i thought cos^2 x + sin^2 x = 1 had the same rule to that but it doesn't



    lol yeah so glad I found out before tomorrow, thanks
    Your exams tomorrow? Not edexcel then I guess?
    And remember the other one, sinx/cosx=tanx does not involve ^2 signs

    GOOD LUCK!!!!
  11. Offline

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    (Original post by geology.is.gneiss)
    Your exams tomorrow? Not edexcel then I guess?
    And remember the other one, sinx/cosx=tanx does not involve ^2 signs

    GOOD LUCK!!!!
    No ocr yep!

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