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# Topic: Unit circle

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 PlanetMath: circle   (Site not responding. Last check: 2007-10-07) Definition A circle in the plane is determined by a center and a radius. The circle consists of all points whose distance from the center equals the radius. A circle determines a closed curve in the plane, and this curve is called the perimeter or circumference of the circle. planetmath.org /encyclopedia/Circle.html   (449 words)

 Unit circle - Wikipedia, the free encyclopedia ; the generalization to higher dimensions is the unit sphere. Relationship of trigonometric functions on the unit circle. In fact, not only sine and cosine, but all of the six standard trigonometric functions — sine, cosine, tangent, cotangent, secant, and cosecant, as well as archaic functions like versine and exsecant — can be defined geometrically in terms of a unit circle, as shown at right. en.wikipedia.org /wiki/Unit_circle   (484 words)

 Unit - Wikipedia, the free encyclopedia Unit circle, the circle with radius 1 centered at the origin Unit (ring theory), an element that is invertible with respect to ring multiplication In category theory, there is a natural transformation called the unit from the identity functor to the composition of two adjoint functors, q.v. en.wikipedia.org /wiki/Unit   (283 words)

 ipedia.com: Circle Article   (Site not responding. Last check: 2007-10-07) If only (part of) a circle is known, then the circle's center can be constructed as follows: take two non-parallel chords, construct perpendicular lines on their midpoints, and find the intersection point of those lines. A part of the circumference bound by two radii is called an arc, and the area (i.e., the slice of the disk) within the radii and the arc is a sector. Every triangle gives rise to several circles: its circumcircle containing all three vertices, its incircle lying inside the triangle and touching all three sides, the three excircles lying outside the triangle and touching one side and the extensions of the other two, and its nine point circle which contains various important points of the triangle. www.ipedia.com /circle.html   (980 words)

 The Unit Circle The circle's center is at the origin, and its circumference comprises the set of all points that are exactly one unit from the origin while lying in the plane. To use the unit circle, we put the vertex of an angle at the center of the circle with the first side of the angle extending along the x-axis from the vertex toward the right. The circle's radius being one unit in length is important now, because the sine and cosine are defined as the opposite or adjacent (respectively) over the hypotenuse. www.humboldt.edu /~dlj1/PreCalculus/Images/UnitCircle.html   (660 words)

 Identify Fractions With Circles The numerator tells us how many of the parts in the unit are to be taken. The denominator tells us the total number of equal parts into which the unit is divided. In this example there are 7 equal parts in the circle. www.visualfractions.com /EnterCircle.html   (101 words)

 Trigonometry:In simple terms - Wikibooks, collection of open-content textbooks In principle, all angles and trigonometric functions are defined on the unit circle. The center point of the unit circle will be set on a Cartesian plane, with the circle's centre at the origin of the plane — the point (0,0). So for any given triangle inscribed in the unit circle we would have an angle whose value is the distance of the triangle-leg on the x-axis. en.wikibooks.org /wiki/Trigonometry:In_simple_terms   (789 words)

 Assignment 1 -- The Sine Function The unit circle is a circle with a radius of one. In the unit circle, the radius is one unit. If one views the unit circle and travels counter clockwise pi/2 radians the height of the triangle is one, when traveling pi/2 radians from 0 clockwise the height of the triangle is -1. jwilson.coe.uga.edu /emt668/EMAT6680.2003.Su/Shea/assign1js/sinefunction.html   (1591 words)

 Topics in trigonometry:  The circle A CIRCLE IS A PLANE FIGURE bounded by one line, called the circumference, such that all straight lines drawn from the center to the circumference, are equal to one another. A diameter of a circle is a straight line through the center and terminating in both directions on the circumference. of the circle is to the area of the square. www.themathpage.com /aTrig/circle.htm   (570 words)

 Area & Circumference of a Circle by Archimedes   (Site not responding. Last check: 2007-10-07) The perimeter of an inscribed polygon approaches the perimeter (circumference) of a circle as the number of sides on the polygon increases. C = the sum of the "bases" of the inscribed isosceles triangles, the limit of which is the circumference of the circle. With the unit circle (red) as the basis, Archimedes used the limiting process on the area and base of polygons (n-gons) inscribed in circles (as n approaches infinity) to determine www.math.psu.edu /PSUmathhome/courses/maserick/circle/circleapplet.html   (450 words)

 FUNDAMENTAL TRIGONOMETRY The first circle is called the unit circle, with a radius of one. A circle whose radius is one (r=1); a circle with the equation x² + y² = 1; a circle with a circumference of 2 The length of the line connecting the opposite and adjacent; in Trigonometry, a multiple of the unit circle radius; represented in algebra by the symbol c; according to the Pythagorean theorem, a² + b² = c². barbaria.com /god/math_physics/basic/trig.htm   (795 words)

 Unit Circle and Trigonometric Functions sin(x), cos(x), tan(x) Using the unit circle, you will be able to explore and gain deep understanding of some of the properties, such as domain, range, asymptotes (if any) of the trigonometric functions. The relationships between the graphs (in rectangular coordinates) of sin(x), cos(x) and tan(x) and the coordinates of a point on a unit circle are explored using an applet. Using the unit circle, do you think that any of the coordinates of a point on the circle can be larger than 1 or smaller than -1. www.analyzemath.com /unitcircle/unitcircle.html   (414 words)

 TRIGONOMETRY FOR STATICS-Part 2 To do this, draw a circle of unit radius, as shown in the figure. One denotes the quadrants of the unit circle as shown in the figure. The unit circle can also help one memorize the values of the trigonometric functions. em-ntserver.unl.edu /Math/mathweb/trigonom/trigsB97.html   (372 words)

 SparkNotes: SAT Math Level 2: The Unit Circle The unit circle is a circle whose center is the origin and whose radius is 1. The most useful and interesting property of the unit circle is that the coordinates of a given point on the circle can be found using only the knowledge of the measure of the angle. of a circle, while a radian is equal to the angle that intercepts an arc of the same length as the radius of the circle. www.sparknotes.com /testprep/books/sat2/math2c/chapter9section6.rhtml   (570 words)

 PlanetMath: unit disk   (Site not responding. Last check: 2007-10-07) The unit disk in the complex plane, denoted See Also: conformal Möbius circle map theorem, Schwarz lemma, complex, upper half plane, unit disk upper half plane conformal equivalence theorem This is version 5 of unit disk, born on 2003-05-12, modified 2003-05-13. planetmath.org /encyclopedia/UnitCircle.html   (59 words)

 Common Angles Around a Circle   (Site not responding. Last check: 2007-10-07) The circle below can be thought of as being divided into angles that are integer multiples of 30, 45, 60, and 90 degree angles. Click one of the points on the circle to see the angle and its measurement in both degrees and radians. The angles marked on this circle represent common angles that are often used in introductory geometry and trigonometry problems. id.mind.net /~zona/mmts/trigonometryRealms/CommonAngles1/CommonAngles1.html   (130 words)

 SparkNotes: SAT Math Level 1: The Unit Circle The most useful and interesting property of the unit circle is that the coordinates of a given point on the circle can be found using only the measure of the angle. Point P is the endpoint of a radius of the unit circle that forms a 30º angle with the negative x-axis. The unit circle also provides a lot of information about the range of trigonometric functions and the values of the functions at certain angles. www.sparknotes.com /testprep/books/sat2/math1c/chapter9section5.rhtml   (518 words)

 Evolution of Math into Art via Mobius Transformations n of the circles are tangent to the unit circle and arranged around the circle in such a way that each of the circles is tangent to the two The (n+1)st circle is has its center at the origin and is tangent to the first n circles. (How many circles would that be?) So, as a safeguard, if you type in 10 or more circles and 4 steps and "show all steps, y or n", the program restricts you to n (that is you cannot see all stages for high numbers of circles and the maximum number of steps). myweb.cwpost.liu.edu /aburns/flash/evmthart.htm   (484 words)

 Key Values of the Unit Circle Measure π/4 units up from the positive x-axis on the unit circle and drop a line segment down to the positive x-axis from that point forming a right triangle. Now that you see how the key values of the unit circle are derived, you may be wondering how you are going to remember them. After practicing labeling a unit circle, you should also practice counting in radians on the unit circle. www.lcc.edu /~lshears/math122/handouts/lecture_notes/unit1/keyvalues   (769 words)

 Earth Math The purpose of this applet is to illustrate the relation between the unit circle and how the trigonometric functions are defined. Drag the point around the unit circle, clockwise or counterclockwise, as many times as you want. A red line whose length is the value of the chosen trigonometric function will be displayed on both the unit circle and the graph. earthmath.kennesaw.edu /main_site/tool_chest/trig_func.htm   (177 words)

 UNIT CIRCLE APPROACH TO TRIGONOMETRIC FUNCTIONS   (Site not responding. Last check: 2007-10-07) You can begin with the standard introduction to (or a review of) the unit circle approach to defining the two basic circular functions; the sine and the cosine. Using a unit circle figure, the arc length t is measured counter-clockwise around the circle starting from the point Use the TRACE feature to move the cursor around the unit circle and watch the values of the parameters displayed on the bottom of the screen. www.uwc.edu /dept/math/gc-sig/kschmd1.htm   (290 words)

 Trigonometry or Trig: Math This drawing shows the unit circle; that is, a circle around the origin, with radius one. One more example of the usefulness of the unit circle: textbooks often give you an angle, and ask you if the sine and cosine are negative or positive. moves from zero to ninety, the y-coordinate on the unit circle is constantly increasing. www.ncsu.edu /felder-public/kenny/papers/trig.html   (2655 words)

 Lesson Plan Properties of the unit circle and definitions of circular functions will be applied. T.3 The student will find without the aid of a calculating utility the values of the trigonometric functions of the special angles and their related angles as found in the unit circle. In this activity, students will use Geometer's Sketchpad to manipulate the unit circle and use it to determine the values of the trigonometric functions of special angles. filebox.vt.edu /users/nkezmars/LessonPlans/UnitCircle.htm   (684 words)

 Preliminaries Because a transcendental function is not defined using a finite sequence of standard arithmetic operations, schemes other than arithmetic usually specify the evaluation of such functions. If the student is able to follow the unit circle construction, the introduction of the graph of sine may confound their understanding. On the other hand, a unit cylinder ties the unit circle directly to the graph of sine and also connects the graph to the identity function www.accd.edu /sac/math/FACULTY/RFerguso/cylinder_preliminaries.htm   (214 words)

 Homotopy Classes of the Circle Suppose a path loops around one circle 19 times, then around another circle -22 times, then around another circle 12 times, and so on, such that the cumulutive sum of the absolute value of these degrees is unbounded. The smallest circle has radius r, and points arbitrarily close to u have images that are at least r units away from f(u), whence the path is not continuous at u. The winding number of a closed path in the unit circle is its degree, as defined above. www.mathreference.com /at,degree.html   (1307 words)

 Using the Graphing Calculator to Investigate the Unit Circle Listed below are two investigations that will allow you to investigate the workings of the unit circle and the relationship between the unit circle and the trigonometric graphs. The Unit Circle and the Trigonometric graph will be drawn simultaneously. Trace between the unit circle and the trig curve to see the relationships between the graphs. mathbits.com /MathBits/TISection/Trig/unitcircle.htm   (112 words)

 The unit circle -- Topics in trigonometry Let us now consider a circle of radius 1, which is called a unit circle. On the unit circle — r = 1 — the functions take a particularly simple form. To evaluate a function at a quadrantal angle, the student should sketch a unit circle. www.themathpage.com /aTrig/unit-circle.htm   (752 words)

 [No title] ¥      óó  Ä Ð ?  Ð The Unit Circle The unit circle is a circle with a radius with length one unit. In this activity, we are going to explore various angles in degree and radian form using a unit circle. The point on the circle is moved by placing your mouse on top it, holding down the left button on your mouse, and dragging the point. www.augustatech.edu /math/molik/UnitCircle.doc   (403 words)

 Solving Trigonometric Equations It is easier to see this in a diagram of the unit circle. Any angle A whose terminal side passes through an intersection point of the horizontal line and the circle will be a solution to the equation sin A = y. The horizontal line y = - 2 / 3 intersects the unit circle in the third and fourth quadrants. jwbales.home.mindspring.com /precal/part5/part5.5.html   (493 words)

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