Angle division without protractor and measuring slider?
481919
It is impossible to trisect an arbitrary angle using only compass and straightedge (but bisection is possible). No there is no mathematical technique (i.e a theoretical construction technique to do so, even if impractical). It cannot be done exactly. The best that can be done is approximation. One can imagine, I suppose, a radial arm (our radius rotating about a fixed  point) whose rotation speed was controlled very precisely by a computer and the speed could be extremely slow and a laser could be used with a super accurate quartz timer to 'print' a dot at fixed intervals thus dividing an arbitrary angle as desired. Certainly, technologically feasible, but I haven't heard anything about it, and it would be a technological technique, not a mathematical "breakthrough".
119218
For distance, just add the magnitudes of all distances the object travelled.\n\nfor displacement, us the formula\n\nd = sqrt ( d1^2+d2^2+2*d1*d2*cos(angle between d1 and d2) )
254484
to measure: the point of the angle should be in the center of the protractor where the 90deg. mark and the horizontal line meet.  place the horizontal line over one line of the angle.  the tick mark or number that the second line points to indicates the angle.
114899
There's a great tutorial/newsletter on using the RAD Video Tools to do just that.  I've included the link below.  It's a free download and the steps are well explained by PapaJohn.
881785
10 degrees\nor \npi/18 radians
1010902
This is  basic\nslope= m=(y2-y1)/(x2-x1)=(12-7)/(8-6)=5/2\nangle=arctan(5/2)
23041
You can measure the distance from the angle to the pole and use trigonometry.  But it may be easier to just move nearer or farther from the pole until the angle is 45 degrees; then the distance to the pole will equal the height of the pole (and you won't need a trig table).
920579
use synthetic  divsion method \ni think this link would help\nhttp://www.purplemath.com/modules/synthdiv.htm
730499
If I have the picture correct, then angle ADC measures 90 degrees (because CD is a perpendicular bisector). the ratio x/3 meters could be set equal to the (sin/cosine/tangent...not sure if I can give you that information or not) of 90 degrees. Find the (sin/cosine/tangent) of 90, and cross-multiply your two ratios (x/3=somethingof90/1). Solve for x.
557771
Draw a straight line.\nDraw a good cuve (mirror), using a compass or a protractor(for later mark a point as centre and place the protractor on this point coinciding with the axis.)\nThe curve should be of equal length on each side of principle axis.\nNow mark the pole, radius and focal point (twice the radius).\nIn case u use protractor, take focal lenght as twice the distance between the marked pont and pole.\n\nRemember how the rays reflect/refract, and accordingly draw two incident and two reflected/refracted rays.\nGive the standard sign convention...I hope plane mirror and prism are easier.
1106173
The direction (angle) of |u| and |v|?
757335
x=r(t-sint) and y= r(1-cost) are the parametric equations of the cycloid where r is the radius of the rolling circle and t is the angle through which the radius of the circle has turned from its starting point. The angle t must be measured in radians.\n\nFor simplicity let r =1 so that we have the unit circle.\nwith t=60 = pi/3 we get\nx = pi/3-sin(pi/3) = pi/3 -(sqrt 3)/2\ny = 1-cos (pi/3) = 1- 1/2 = 1/2\n\ndy/dx= sint/(1-cost)\n=[(sqrt 3)/2]/(1/2) = 3^0.5 (at the point where t= 60= pi/3)\n\nFrom this , you can find the slope at any point define by the parameter t.\n\nb) The tangent is horizontal when t= pi and is perpendicular at the cusp which occurs at 2pi and multiples thereof. The maximum value  is 2r (or 2 for the unit circle). The length of the base of the arch is 2pi *r or just 2pi for the unit circle.
877622
ok...is what id imaigne you want is a ruler and compass construction of a line segment and you want to divide it into 4 equal parts...this isnt so bad\n\nis what you need is the bisector construction...and you do this 3 times...so you have your segment...go get yoru compass!\n\nok, now that you have your compass...put the pointy part of the compass on one of the segment endpoints...open teh compass so its open to a little more than half the length of the segment...draw an arc above and below the segment, then do the same thing with the other end point...\n\nyou now notice that those two arcs you drew intersect at 2 points...and if you connect those two points of intersectoin you would bisect the line....ok, so we have divided the line in half...well we need to do that again...\n\nso now go back to the endpoint you started on, and put the pointy end of the compass on the endpoint and open the compass to slightly more than half the distance from the endpoint to the bisector...arc above and below the line, repeat teh steps at the place where the bisector cuts the line...you would noice that these two arcs will intersect above and below the line...and you connect those points, and you have now split one half of the line into quarters...do the same thing for the other half\n\nhope this helps.\n\nmatttlocke
450833
join the 2 pointz frm da arc vit da radius.measure out da value of da angle forned here.then substitute da values 4 this formula:  2*pie*radius/da angle u measured\n\nhappy solvin!
716372
1 and 2 are easy. I'll help with #3.\n\n3. You need I, the rotational inertia. From a table in my physics book, I = MR^2 for the reel. You need to convert the force to torque, T = F*R. \n\na. Then you can get the angular acceleration, alpha, from \nT = I*alpha\n\nb. In t = 0.25 s, omega will reach alpha*t. The angular displacement, theta, will be (1/2)*omega*t. From that and the circumference you can get the line drawn from the reel.
6838
∫xSec(x²)²dx = .5Sin(x²)/Cos(x²)
1048040
A traditional goniometer is a protractor with extending arms. To use a goniometer:\n(1) Align the fulcrum of the device with the fulcrum or the joint to be measured\n(2) Align the stationary arm of the device with the limb being measured\n(3) Hold the arms of the goniometer in place while the joint is moved through its range of motion\n\nThe degree between the endpoints represents the entire range-of-motion.