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

  1. 0
  2. 2
asked by sweetG
  1. Sorry i forgot some of the theta signs again in question 3 as well
    I hope its still understandable

    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.

    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.

    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)

    or

    you might want to Google Heron's Formula

    or

    line up the points

    2 7
    3-3
    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

    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 :)

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

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

    posted by Jen
  8. it is an equation

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

    posted by Anonymous

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