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Math Help - Trigonometry help.

  1. #1
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    Trigonometry help.

    These are not really H.W questions but i have an exam coming very soon and i have some problems:
    Trigonometry:
    i) Express as a single trigonometric function sinxcosxsecx (i keep on going in circles in this one)

    ii) A square B, has a diagonal 2x. A square C has twice the area of square A. Find in terms of x, the perimeter of the squre C.

    Help would be much appreciated.
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  2. #2
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    i)  sin\,x\, cos\,x\,sec^2x = \frac{sin\,x\,cos\,x}{cos^2\,x} = \left(\frac{sin\,x}{cos\,x}\right) \left( \frac{ {cos\,x}}{ cos\,x} \right)=tan \,x

    ii) A square has 4 equal sides. The diagonal cuts the square into two isosceles, right angled triangles.
    Let side of Square B = a. By pythagoras's theorem,  a^2 + a^2 = (2x)^2
     2a^2 = 4x^2
    a^2 = 2x^2
    a = \sqrt{2}x

    Now Square C has area twice Square B.
    Area Square B = a^2
    Area of Square C = 2a^2

    From the working above, we know 2a^2 = 4x^2

    Therefore Area of Square C is (Side C) =  4x^2 where Side C is a side of square C

     Side \,C = \sqrt {4x^2} = 2x
    Perimeter = 4(Side C) = 4(2x) = 8x.

    Note: Thank you masters for pointing out that I haven't completed the question. Its very late in my time zone, and I misread the question.
    Last edited by Gusbob; May 7th 2008 at 08:22 AM.
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  3. #3
    A riddle wrapped in an enigma
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    If the area of square [LaTeX ERROR: Convert failed] , then each side = 2x. Therefore, the perimeter would be 4(2x) = 8x
    Last edited by masters; May 7th 2008 at 08:47 AM.
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  4. #4
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    Wow, thanks alot for the quick reply. I totally forgot that
    secx=1/cosx!
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