Find all polar representation of Cartesian point (-1,1)?
930129
r = √1² + (-1)² = √2\nθ = arctan(1/-1) = -π/4 ± n2π, where n is any integer.
1149867
We have x=rcos(θ), and y=rsin(θ).  \n\n\nTherefore x=4sin(θ)cos(θ) and y=4sin(θ)sin(θ).  \nAnd x^2+y^2= 16sin(θ)^2(cos(θ)^2+sin(θ)^2) =16sin(θ)=4y.  \nThus x^2+y^2-4y+4-4 =x^2+(y-2)^2-4=0 and x^2+(y-2)^2=4.\n\nAre you sure the second one is given by:\nρsin(θ)=2cos(θ) and not ρsin(φ)=cos(θ)?\n\nif it is ρsin(φ)=2cos(θ), then first notice that φ≠kπ for any integer k.\nThen we have ρ=2cos(θ)/sin(φ)\nNext we have x=ρcos(θ)sin(φ)=2cos(θ)^2, and y=ρsin(θ)sin(φ)=2cos(θ)sin(θ).\n\nThus x^2+y^2= 4cos(θ)^2(cos(θ)^2+sin(θ)^2) =2x,\nand x^2-2x+1-1+y^2= (x-1)^2-1+y^2=0,\nso (x-1)^2+y^2=1
791344
R = [ a^2 + b^2 -2*a*b* cos(theta), where  theta is the angle between a and b.\nIf a and b are fixed,\nR is max when  cos(theta) is min.   \nMin value of cos(thete) = -1  at  thete = 180 degree
513183
Yes.  Assuming that you are familiar with 2-dimensional rectangular (Cartesian) vectors, (x,y) axes, then the polar coordinates are given by \nr=(positive)square root of (x^2+y^2), and\ntheta=the angle whose tangent = y/x, where\n\nr is the length of the vector and\ntheta is the direction of the vector with respect to a given reference direction.\n\nAddition and subtraction of vectors are simpler in rectangular coordinates while multiplication and division of vectors are simplified by transforming to polar coordinates.\n\nPolar coordinates are even simpler if radians are used for the angles instead of degrees.
664950
In the polar coordinate system r is always positive. It´s the distance from the origin to the point. \n\nThe transformation to rectangular (or rather carthesian) coordinates is as follows:\n\nx = r cos (theta)\ny = r sin (theta)\n\nSo assuming (r,theta) = (5,52 deg) I find\n\nx = 5 cos (52 deg) = 3.08\ny = 5 sin (52 deg) = 3.94 (both rounded off to two decimals)
627342
ok, this is found in the 4th quadrant, the order is as follows\n\n(x,y) 1st\n(-x,y) 2nd\n(-x,-y) 3rd\n(x,-y) 4th\n\nhope this helps\n\nmatttlocke
909745
Focus on -(x+1).\nIt's like multiplying every term inside the bracket by -1. Hence you're going to get -x-1.\n4 - x - 1 = 8\n3 - x = 8\nAdd x to both sides: 3 = 8+x\nSubtract 8 from both sides: -5 = x\n\nHope this helps :)
1106173
The direction (angle) of |u| and |v|?
1149797
The first one is (-5, 3). I don't remember how to do the others.
561927
Y - Y1 = M(X - X1)\n\nY - 4 = -2(x + 1)\nY - 4 = -2x - 2\n\nY = -2x + 2
768593
To find the inverse of this relation, reverse the coordinates of the ordered pairs.\n\nThe answer to this would be\n {(18, -14), (-18, 3), (-1, -2)}
284143
j * sqrt(pi)\n\nj = i; which is imaginary number which is sqrt(-1)\nsqrt is "square root"
311149
y=-1\nEDIT-OOPS-forgot about the negative part-more info:\nas in the point = (0,-1)\n\nthis is because the 1 part int he equation is the "B" in y=mx+b.  b is your y-intercept.  if b is negative, then your y-intercept is negative
801068
-4(-1)^2 - 3(-1)\n-4(1) - -3\n-4 + 3\n= - 1
24161
The square root of a negative number is an imaginary one.  The square root of -1 is known as i.  Negative square roots work out like positive ones, only with the i, so SqRoot(-4) = 2i and SqRoot(-64) = 8i.
465985
1 - D\n2 - B\n3 - C\n4 - C
530897
Plot and join these points : (x,y) = (-1,-5);(0, -4);(1,-3);(2,-2);(3,-1);(4,0);(5,1).