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Math Help - 2 questions

  1. #1
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    2 questions

    Hi i'm stuck on 2 questions and wondering if you can help me out.

    1 ) The area of a sector of a circle with radius r cm is fixed at 16 square centimetres, show that the perimeter P cm of the sector OPQ is given by
    P = 2 (r + 16/r).


    2 ) Express cos x + 2 sin x in the form k cos (x - a) where k > 0 and 0 < a < 360.

    Hence solve the equation cos x + 2 sin x = 1, where 0 < x < 360


    in question 2, i couldn't put in degrees signs, the a = alpha, and the "<"s used are the 'less or the same than' - i didn't know how to write them.


    thanks for any help
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Ok

    Quote Originally Posted by Maths409 View Post
    Hi i'm stuck on 2 questions and wondering if you can help me out.

    1 ) The area of a sector of a circle with radius r cm is fixed at 16 square centimetres, show that the perimeter P cm of the sector OPQ is given by
    P = 2 (r + 16/r).


    2 ) Express cos x + 2 sin x in the form k cos (x - a) where k > 0 and 0 < a < 360.

    Hence solve the equation cos x + 2 sin x = 1, where 0 < x < 360


    in question 2, i couldn't put in degrees signs, the a = alpha, and the "<"s used are the 'less or the same than' - i didn't know how to write them.


    thanks for any help
    Ok I will give you a hint the area of a sector is A=\frac{1}{2}r^2\theta
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  3. #3
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    any posibility of you showing me a few lines of what to do?

    my brain is completely dead and this needs to be finished asap
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  4. #4
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    Quote Originally Posted by Mathstud28 View Post
    Ok I will give you a hint the area of a sector is A=\frac{1}{2}r^2\theta
    1. Use the above formula to get \theta in terms of r.

    2. Arc length = \theta r.
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  5. #5
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    Quote Originally Posted by Maths409 View Post
    [snip]
    2 ) Express cos x + 2 sin x in the form k cos (x - a) where k > 0 and 0 < a < 360.

    Hence solve the equation cos x + 2 sin x = 1, where 0 < x < 360

    in question 2, i couldn't put in degrees signs, the a = alpha, and the "<"s used are the 'less or the same than' - i didn't know how to write them.


    thanks for any help
    Use the compound angle formula to expand k \cos (x - a).

    Now equate the coefficient of cos x with 1 and the coefficient of sin x with 2 to get two equations that you solve simultaneously for a and k.
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