Can anyone explain 'normalised measure on the circle' please!?
605625
The ratio of any measure of the circle is said to be normalized when it is divided by the radius, such that the resultant measure is equivalent to the corresponding measure of a unit circle (circle of radius = one).
642048
Think about it.  If you have an angle drawn on a sheet of paper and you rotate one segment, will the length of the segment still be the same?  Yes, all you're doing is changing its position, the length remains the same.  \nWill the measure of the angle remain the same?  Of course not, by rotating one segment you're automatically changing the angle from it to the other segment.  \nFinally, if you rotate a segment, is it still oriented the same?  No way!  You just changed its position, how can it still be oriented the same way?
855373
it goes around the circle twice, therefore it is a coterminal angle to the original angle.  all trig values are the same.  the only difference is that the degrees goes up by 720.\n\nadding or subtracting multiples of 2 pi just go around the circle.  since pi=180 degrees, add or subtract 180*the number of pi's.  \n\nyummy pumpkin pie :)
481336
well, ok, i see lots of complicated answers...but here is the answer in simple terms\n\nthe radius measures teh distance from the center to its boundry...it doesnt matter what the coordinates of teh boundry are because we have to use the distance formula to find it which is\n\nd = sqrt[(x-x1)^2 +(y-y1)^2]\n\nso from this equation (x1,y1) is the origin (0,0)\n\nso you really have\n\nradius = d = sqrt[x^2 + y^2]\n\nso whatever point you choose the distance must be positive because any numbers squared then added will be positive.\n\nso you would claim, well what if the center wasnt at the origin, well the only difference would be that you would use the original distance equation i mentioned.\n\nSo we can say that all distance (according to the distance equation) must be positive, try it with any points you like, it will always be positive.  Due to the distance equation always being positive, all radii must be positive.\n\nhope this helps\n\nmatttlocke\n\nPS\nand for everyone who says distance cant be negative...they lie\n\nthe magnitude of direction can never be negative the negative does imply direction.  for example, on the number line, we have points -5, and 5, the distance of both of those points from 0 is 5, but if we were plot each point they would be going in opposite directions, and we know this due to the negative sign\n\nso the distance formula means that the distance will always be positive, the negative does tell you direction, ask any mathematician (im working on that) or a physicist and they will tell you the same thing.\n\nBut, a negative and positive radius mean the same thing because the boundry of the circle will intersect all the points at whatever the measure of the radius is in all directions, so i spose you could look at it as negative, but it doesnt really matter.  This would all hold in any 'n' dimension.
524608
Imagine the square of string:\n\nWhat will you do to make it a circle? You would have to bend the sides to form an arc like the way you would bend an archer's bow. For it to become a circle, you have to bend the four sides equally so that the corners will no longer be present.\n\nSo your new circle now will have an area bigger than the square. If you overlap the 2 figures together, you would have a big circle and inside it is a square whose 4 corners touch 4 equidistant points on the circle.\n\nArea of the circle: 64/pi OR 20.3718
418030
Take a unit circle and a point p on the circle. Place the circle so that it is centered at the origin in a Cartesian xy-plane. The cosine of p, cos(p), is defined to be the x-coordinate, or abscissa, of p. The sine of p is the y-coordinate. These functions are the just the projection functions for the unit circle by the standard embedding in the Cartesian plane as described above.\nIt is common to give the points p on the 1-dimensional circle the coordinate referring to the arclength between p and the positive x-axis (as measured clockwise). Thus, the point (1, 0) on the unit circle is given the native coordinate (0), or 0 for short. Inversely, the point 0 in the unit circle has Cartesian coordinates (cos(0), sin(0)). Since the circumference of a circle is 2Pi, a point that is a quarter of the way around the circle from the positive x-axis is given the coordinate 2Pi/4 = Pi/2 and so forth. This system of coordinates is called radians and is the native way of measuring angles, as each angle corresponds to a unique point on the unit circle.\nThis relationship can be seen by drawing a radius from the origin to mark the angle from the positive x-axis and assigning that angle to the radian measure of wherever it intersects the unit circle. There are more analytical reasons as well, as you go on to study calculus.\nThe radius drawn above also gives the relationship between these circular projection functions, and the way one first encounters trigonometric functions, as ratios of the sides of right triangles. Now you should be able to visualize the triangles inside the unit circle (or any larger circle, dependent on the triangle's hypotenuse), and see why the trigonometric functions are cyclic in 2Pi, and derive some properties of the trigonometric functions that are not easily apparent from just looking at right triangles.\nIt is now however easy to see why all the basic trigonometric functions have a neighbor with prefix co-. The cosine is short for complementary sine. This is because the cosine of a point is obviously the same as the sine of the complementary angle.\nThe tangent function is so named because it is the length of a certain tangent to the circle; a tangent drawn from the positive x-axis to where it meets an extended radius of the circle. You may be able to work out the equation tan(p) = sin(p)/cos(p) from the geometry involved.\nThe arc trigonometric functions are so named because they measure arc length; they give you back the radian measure of the sine or cosine when you restrict these functions to one hemicircle (otherwise you get two possible answers).\nThe secant function does not give you an arclength; it is another function of points on the unit circle (and thus by our unit circle coordinate system, it is a function of arc length). In the right triangle formed by the tangent to the circle, the secant is the length of the hypotenuse. The arcsecant function returns the arc length on the unit circle that the secant intersects. See the sources below for illustrations.
456513
A=pi*x*y \n\nwhere x is small radius from centre to circumference and y is large radius from centre to circumference.
658093
Given the nature of the values I am assuming they are identifying the circumference.    \nC = 2 * pi * radius = pi * diameter.   \nSo, to find the diameter we would divide out the pi or use 3.14 to get to the diameter for each value.  \nHope this helps.
195018
Draw all this out so you can see it - it won't be to scale, but don't let that fool you.....\n\n\ndiameter = 50cm (radius = 25cm)\nchord = 20cm from diameter (thus it's 20cm from the center)\n\nOK, you'll need to assume that the line segment forming the diameter touches the chord at point B on the circle - i.e. we'll say the diameter is line segment AB and the chord is line segment DB. \n\nC is the center of the circle, so we have radius CB = 25cm. \n\nAlso, we'll have line segment CE drawn perpendicular from the center (C) to point E on the chord, forming a right angle and thus *bisecting* chord DB.\n\nYou have the hypotenuse of triangle ECB (radius CB) as 25cm, and side EC as 20cm (distance from the center to the chord - always perpendicular).\n\nLine segment EB will be the second side of a right triangle, so your formula:\n\nEC^2 + EB^2 = CB^2\n20^2 + EB^2 = 25^2\nEB^2 = 25^2 - 20^2\nEB^2 = 625 - 400 = 225\nEB = 15cm\n\nSince EB = half the length of the chord DB, DB = 2*15cm = 30cm.
555699
I think I can help you with this one... I learned how to do it in Kindergarten.\n\nPull your head out of your ass and measure.\n\nGood Luck!
1158388
In Euclidean plane geometry, π(Pi) is defined either as the ratio of a circle's circumference to its diameter, or as the ratio of a circle's area to the area of a square whose side is the radius. π may be defined in many other ways, for example as the smallest positive x for which sin(x) = 0. See other formulas below. All these definitions are equivalent.\n\nArea of Circle = Pi.(Radius)^2\nPerimeter of Circle (Circumference)=2.Pi.Radius.\nYes .. it has someting to do with Statistics :\n\nIn probability and statistics, there are many distributions whose formulæ contain π, including:\n\nprobability density function (pdf) for the normal distribution with mean μ and standard deviation σ : \nhttp://en.wikipedia.org/wiki/Pi
1137727
I like the joke!  To play along, I define:\nr = metric r  and \nd = metric d\n\nV = (pi/3)*(d^2)*(3r - d)\n\nThis will work for the tank being any fraction of a sphere, not just 1/2
197839
No. 99 is not correct. \nHasn't your teacher taught you trigonometry? If not the graphic approach you're following offers an approximation but Trig is best.\n\nYou are right to consider a polygon with 36 sides enscribed in a circle as an approximation the area enclosed by a circle would be PiR^2 and you could compute R the radius from the formula for the circles circumference 2PiR=36, giving radius 5.72m, hence area 103 m^2.\n\nThe biggest square would have side 9m wide enclosing area of 81m^2. So you know the correct annswer must be the circular polygon and it's area must be approimately but slighly less than 103m^2.\n\nThe circular polygon comprises 36 adjacent triangles. To find he area of one triangle you need to realise each one is "made up" of two internal right angle triangles, each with an internal angle of 5 degrees and base length 0.m.\n\nThe area of one internal right triangle will be 1/2 basex height = 1/2 x0.5x A\n \nThe trigonometric function Tan is defined as the ratio of the opposite side to the adjacent side A. Therefore:\n\nTan 5 degrees= 0.5 / A\n\nRearranging gives A = 0.5 / Tan5degrees (=5.715 m using a calculator)\n\nSince each of the 36 segments contains 2 internal triangle the area of each is: 2 x 1/2 x 0.5 x A = A/2\nSo area for all 36 = 36/2 A= 18A = 102.87 m^2
300944
The symbol  was first introduced by William Jones [7,8] in 1706 to denote the ratio between the perimeter and the diameter on any given circle. In other words, dividing the perimeter of any circle by its diameter always gives the same answer, and this number is defined to be . A 14-digit approximation of  is given by \n\nOver human history there were many attempts to calculate this number precisely. One of the oldest approximations appears in the Rhind Papyrus (circa 1650 B.C.) where a geometrical construction is given where  is used as an approximation to  although this was not explicitly mentioned.\n\nIt wasn't until the Greeks that there were systematical attemps to calculate . Archimedes [1], in the third century B.C. used regular polygons inscribed and circumscribed to a circle to approximate : the more sides a polygon has, the closer to the circle it becomes and therefore the ratio between the polygon's area between the square of the radius yields approximations to . Using this method he showed that  .\n\nAround the world there were also attemps to calculate . Brahmagupta [1] gave the value of  using a method similar to Archimedes'. Chinese mathematician Tsu Chung-Chih (ca. 500 A.D.) gave the approximation .\n\nLater, during the renaissance, Leonardo de Pisa (Fibonacci) [1] used 96-sideed regular polygons to find the approximation
746093
It's straight ahead geometry.\nDraw a circle with center O.  Draw a diameter horizontally through the circle. Label the left intersect as A and the right intersect as B.  Now draw a vector from O to a point P on the circle.  What tdo you know about triangles AOP and BOP in terms of the angle the vector makes with the diameter?  Use law of sines, law of cosines, trig, etc. to show that angle APO and angle BPO add up to 90 degrees and your done.\n\n\nDoug
739875
The formula for the circumference of a circle = pi x diameter.\n\nYou may have a value for pi like 3.142 .......(this is the one I remember)\n\nYou can tell by looking at the answers, that the answer is approx 21  (rather more than 3 x a tiny bit less than 7)\n\nAt some stage during the lesson that preceded this homework, there must have been a discussion about the appropriate number of decimal places to use.\n\nThe diameter of the circle was measured at some time.  It was given as 6.94 cm.  The measurement was considered good to 2 decimal places.  The value of the circumference is based on a calculation using this measurement to 2 dec pl, so the answer is good to 2 dec pl  = 21.80\n\nThe difference between 21.8 and 21.80 is precision.  The extra place of decimals shows greater precision.\n\nSome people know the value of pi to twenty decimal places.  You may multiply the value of the diameter by pi to 20 pl of decimals.  The answer has no meaning beyond the 2 places of decimals used when the diameter was measured.
970313
r=radius\nd=diameter\n\n1 C=2r(pi)\n2 C=d(pi)\n\n(Same thing because 2r=d)