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I need a smart person to answer this, please, I REALLY need to understand this
a smart person eh..... hmmm
the slope of L1 with respect to L2 suggests to me that it is a relative answer. If L2 were flat, what would the slope of L1 be with it..
y=x has a slope of 1, which is a tan(45)
ok, I know this, but where do I go from here?
y = 2x... has a slope of 2....
so it is 2 :)
i aint determined that yet :)
it is the angle of slope 2 - slope1 but you use the "angles" and not the slopes
what angle has a tan^-1(2)?
oh, so, basically, the slope of L1 in relation to slope L2 will be 1, right?
I am really bad at this sorry... forgot all the high school stuff
tan(63.43) = 2 not really, since we have rotated the axis by a certain degree, we need to determine the degrees involved, then you trig stuff to re dress the problem
.... we dont need the angles perse, just their ration....
isn't there a simple way?
cos(a-b) = cos(a)cos(b)-sin(a)sin(b)
cos(a) = 1/sqrt(2) cos(b) = 1/sqrt(5) sin(a) = 1/sqrt(2) sin(a) = 2/sqrt(5)
cos(a-b)=1/sqrt(2) * 1/sqrt(5) - 1/sqrt(2) * 2/sqrt(5)
1/10 - 2/10 = -1/10
might be better to work it in tans :) that way we get a new "slope"....tan = slope by the way
tan(a-b) = tan(a)-tan(b) ----------- if I recall correctly 1+tan(a)tan(b)
tan(a) = 1/1 tan(b)=2/1
hold up, make a the bigger one... tan(a) = 2; tan(b)=1 2-1 ---- = 1/3 right? 1+2
the new slope is 1/3 :) what was the second part?
equation of the line L1 in relation to eq of the line of L2
y=(1/3)x + b just gotta determine where the lines intersect and use that as a parameter for the new system....
they originally intersect at x=-1; y=-1
the new point of intersection is the length of -sqrt(2)....
so the new coord to fill in is (-sqrt(2),0)
0 = (1/3)(-sqrt(2)) + b b= sqrt(2)/3 y = (1/3)x - (sqrt(2)/3) should be it
why sqrt(2)? the original lines cross at (-1,-1) when we rotate the axis to accomodate the new axises.... that point is still there, but we use the distance of it from the origin as the x intercept
oh, ok, got it
1-1-sqrt(2) is the triangle of a 45 degree..
how did you get so good at maths?
by messing up alot lol
my son is nagging me for the laptop....ciao :)