Maths - More than one question please help me

Hi everyone :)
I need a lot of help. I have many questions i don't get how to do and even if you can help me with one of them, I'd truly appreciate it. I really need the help and i gotta hand this in soon so please help if you know how to do any of these questions. Thanks so much !

1) The sides of a triangle are given by the lines:

2x-y+3=0, x-2y-3=0 and 2x+y-11=0.

Find the area of this triangle.

2)Prove the following identities:

a)(cosec + cot)(cosec - cot) = cottan

b)2/1+sin + 1/1-sin = 3sec^2 - tancosec

[sorry i didn't have the theta signs there]

3)Show that cot^2 - cos^2 = cos^2 x cot^2

4)Find all solutions in the interval -180<x<180 degrees to the equation
cosx + sin^2x = 5/4

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asked by sweetG
  1. Sorry i forgot some of the theta signs again in question 3 as well
    I hope its still understandable

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    posted by sweetG
  2. 4) Use the identity sin^2x = 1 - cos^2 x so that your only variable is cos x. Then solve for that.

    cos x + 1 - cos^2 x = 5/4

    cos^2 x - cos x = -1/4
    Let y = cos x
    4 y^2 -4y +1 = 0
    (2y -1)^2 = 0
    y = cos x = 1/2
    What angles x have a cosine of 1/2? 60 degrees is one of them. There is another one too, in the interval they have specified.

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    posted by drwls
  3. You will usually get answers sooner if you limit yourself one question per post. Most of us volunteers don't have time to do several at once.

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    posted by drwls
  4. I will tackle this one for you

    <1) The sides of a triangle are given by the lines:

    2x-y+3=0, x-2y-3=0 and 2x+y-11=0.

    Find the area of this triangle. >

    Equation #1 : 2x-y = -3
    Equation #2 : x-2y = 3
    Equation #3 : 2x+y = 11

    solving #1 and #3 I got A(2,7)
    solving #2 and #3 I got B(5,1)
    solving #1 and #2 I got C(3,-3)

    From here there are many ways to continue.
    Checking for slopes,unfortunately your triangle is not right-angled.

    I don't know what level of math you are taking, but one way is to find the equation of line AC and then use the 'distance from a point to a line' formula to find the altitude from C to that line. Then area is 1/2(base)(height)


    you might want to Google Heron's Formula


    line up the points

    2 7
    5 1
    2 7 and use Area = 1/2(sum of downproducts - sum of upproducts)

    Area = 1/2(-6+3+35 - (21-15+2))
    = 12

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    posted by Reiny
  5. Reiny
    thanks a lot for helping me with the other quesiton too but i got different points because this is how i did it:
    when x = o
    y = ?
    and when y = 0
    x = ?
    and i did that to every equation and got three points and then i plotted the points which gave me a triangle and that's all i got up to Plus im in my last year of highschool so that's the level of maths i was talking about :)

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    posted by sweetG
  6. Thanks for the tip drwls next time i'll keep the questions separate and thanks for your help too

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    posted by sweetG
  7. 2x+1=2x+1 is an expample of a formula or an equation

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    posted by Jen
  8. it is an equation

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    posted by vicky
  9. if y=17-6x

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    posted by Anonymous

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