How do you graph: -cos 2x / 2?
597987
If you are trying to draw it by hand and you already know what cos(x) looks like then it's easy to graph. -cos(2x/2) is just -cos(x) which is an upside-down cos(x). -cos(2x)/2 is a cos(x) graph that is upside-down, because of the {-}, half as tall, because of the {/2}, and compressed by a factor of two because of the {2x}.
935340
= cosx[cosxcosy+sinxsiny]+sinx[sinxcosy-cosxsiny]\n\n= (Cosx)^2cosy+cosxsinxsiny+(sinx)^2cosy-cosxsinxsiny\n\n= (Cosx)^2cosy + (Sinx)^2cosy\n\n= Cosy [ (cos)x^2 + (sinx)^2]\n\n= Cos(y)
967981
y'=cos(x^2e^x)(2xe^x+x^2e^x)\n\ny''=-sin(x^2e^x)(2xe^x+x^2e^x)^2+\n      (2(e^x+xe^x)+(2xe^x+x^2e^x))cos(x^2e^x)
314146
Let y = arccosine x\nthen x = cos y\nfirst put a value for y and get the corresponding value of x\nDraw the graph
772016
x1 >= .2(x1 + x2)\nx1 >= .2x1 + .2x2\nSubtract .2x1 from each side\n.8x1 >= .2x2\nDivide both sides by .2\n4x1 >= x2\nx2 <= 4x1\nNow, assuming x1 is on the horizontal axis (x) and x2 is the vertical axis (y), then\n1) Place a dot at (0,0).  This is the y-intercept.\n2) The slope is 4.  Starting at the point (0,0), move up 4 and to the right by 1.  Place a dot there.\n3) Connect the two points with a straight line.\n4) The graph will be shaded below the line.\nI found this by picking any point that is not on the line.\nFor instance, the point (1,0) is not on the line.\n(1,0) means x1 = 1 and x2 = 0\nx2 <= 4x1\n0 <= 4  Since this is true, you shade the side of the line where this point lies.
819957
Start with a graph of:\nf(x) = x\n\nThat's a straight line going through the origin with a slope of 1.  It should look like a 45 degree angle if you draw it correctly.\n\nNow to transform this to:\nf(x) = | x |\n\nYou have to think of each value smaller than 0.  Rather than -1, for example, you'll have 1.  Rather than -2, you'll have 2, etc.  This is like "mirroring" the graph that is below the x-axis so that it is above the x-axis.\n\nThis results in a "V" shape.  A slope of -1 down to the origin, then a slope of 1 from the origin.\n\nFinally:\nf(x) = | x | - 2\n\nFor every value that results, you now subtract 2.  For example, x = 0, gives -2, rather than 0.  This is true for every point x, making every point y smaller by 2.  It would look like you shifted the whole graph down 2 units.\n\nSo it would be "V" like before, but it would go down at a slope of -1, cross the x-axis at -2, and continue to (0, -2).  Then it would slope up (m=1) through the x-axis at 2 and continue upward.\n\nYou can go to the first link and type 'abs(x) - 2' in the box.  The resulting graph is shown as the 2nd link.
432398
y = -1/2 sin·­­­¹ pi x\nTo graph this, it is easier to rearrange to make x the subject, then turn the graph paper on its side and plot x as a function of y, just remember that y is now positive going left and x is positive going up.\n-2y = sin·­­­¹ pi x\nsin (-2y) = pi x\n1/pi sin (-2y) = x\n\nnow sin (-2y) = sin 2y   (check your trig properties)\n\nso we want to graph\nx = 1/pi sin 2y\n\nnow for the graph  y = a sin bx\nthe amplitude is a and the period is 2pi/b\nso the amplitude is 1/pi\nthe period is 2\n\nPlot your sin function along the y axis. Then turn the paper the right way up. Remember that to be a function, it can only have one value of y for each value of x, you only want a single half S shape, going from y = -.5 to .5, this way the graphs remains a 1 to 1 function.
168710
http://www.graphcalc.com/
904114
First, put your original equation as Y1\n\nFor Y2, type  nDeriv(Y1, x, x)\n\npress the buttons   (math)(8)   to get   nDeriv\nthe buttons (VARS)(1)(1)  to get Y1\n\n\nFor Y3, type  nDeriv(Y2, x, x)\n\nthen just display graph Y3\n\nIt will take quite a long while to graph, better if you manually differentiate the original equation once, then use the nDeriv to do second derivative.
838358
i can't give you the answer but i used my ti-83 and i can tell you the points of the graph...\n(1,0) (2,4) (3,8) (4,0)\n\nHope this helps
635075
Graph X=-4 with dotted lines\n\nthen color everything below the line.
769049
Option a: use one of the fancy calculators around nowadays.\nOption b:\nOk, we need at least a reasonable guess to get going. Lets draw a graph. But how do you draw a graph of 2cos(x) + x? We don't. We draw a graph of 2cos(x), and another graph of -x, and see where they are equal - because thats the point we're looking for. Don't forget to use radians, since you can't add a number to a degree.\nThe solution looks like it is around -1 or so. Now we can do a bit more guessing.\nPutting -1 into that equation gives 0.0806. Lets try -0.9. Whoops - that gives 0.34, which is getting even worse. How about -1.1? Ahha! That gives -0.19, so we know the answer is between -1.1 and -1.0.\nWe can keep narrowing it down in this way. Try -1.05: thats negative, so we're between -1.0 and -1.05. Try -1.02: thats positive, so we're between -1.02 and -1.05. Try -1.03: thats negative, but nearly 0. So we're between -1.02 and -1.03.\nWe're nearly there - try -1.025. thats positive, so we're done! We know the answer is between -1.025 and -1.03, so it must be -1.03 to the nearest 100th.\nThats quite a bit of work, but its not too bad. There are faster ways to do it, but they're a bit more complicated.
816872
Best to plot this on a piece of graph paper; "+i" is  to the right' , "+j" is upwards, "-i" is to the left, "-j" is downwards, all with respect to the origin.\n\n1. Draw the vectors on the graph paper. "u" is in the second quadrant (i is neg and j is pos). "v" is in the fourth quadrant, with (i is pos, j neg) . There are two answers to this question, since you could go from u to v or from u to v in the opposite direction. I always take the angle from zero to "u" and add it to the angle from 0 to "v".  For "u", the tangent of the angle to the vertical axis is 1/4, then angle = 14%. So the angle from zero degrees to the vert axis = 90, and "u"s angle from zero degrees is 90 + 14 = 104 degrees. For "v", the tangent of the angle to the horizontal axis is 4/3 = 1.333.. and the angle = 53 degrees. Therefore the angle from "u" to "v" is 104 + 53 = 157 degrees. (the other answer is 360 degrees - 157 degrees = 203 degrees if you rotate in the other direction).\n\n2. Again use graph paper. 240 degrees is 30 degrees less that 270 degrees (the vertical axis, down) draw a line 10 graph units long. It will be in the third quadrant where i and j will both be negative. At this point you can use a polar to rectangular converter, or do it by hand. By hand: the i side of the triangle formed with the down axis can be found by saying sin(angle) = i/10, and cos(angle) = j/10. The angle is 30 degrees (from vert downwards). so sin(30) = 0.5, and, cos(30) = 0.866; thus i= 0.5 and j = 0.866 (ignoring pos/neg). Since the vector is in the third quadrant, both i and j are negative.\nAnswer = -0.5i -0.866j\n\nHope this helps!
546258
cos2x=cos(x+x)=cos^2x-sin^2x=1-sin^2x-sin^2x=1-2sin^2x\ncos2x=1-2sin^2x  \ncos2x+2sin^2x-sinx=1-2sin^2x+2sin^2x-sinx=1-sinx=0\nsinx=1\nx=2kπ+π/2  ,   k=...,-1,0,1,...
809234
you would plot it on a graph at (0,5) \nor "y-int=5"
411302
cos^2 (2x) is equal to 1-sin^2(2x), remember, sin^2(x)+cos^2(x)=1
975796
draw it on the cartesian graph. then apply the formula.r2 = x2 + y2. Since 2 points are given, then r2 = [13+7]2 + [8+2]2.