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