Question

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

Answer 1

Sorry i forgot some of the theta signs again in question 3 as well
I hope its still understandable

Answer 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.

Answer 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.

Answer 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

Answer 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 :)

Answer 6

Thanks for the tip drwls next time i'll keep the questions separate and thanks for your help too

Answer 7

2x+1=2x+1 is an expample of a formula or an equation

Answer 8

it is an equation

Answer 9

if y=17-6x