As a VBA function, you can use this function in macro code that is entered through the Microsoft Visual Basic Editor. The conversion used for radians and degrees is \(2\pi \text{ rad}=360^{\circ}\), or if you simplify that, \(\pi \text{ rad}=180^{\circ}\). With similar opposite arcs joints in the same plane, continuously differentiable: In studies of rivers, the sinuosity index is similar but not identical to the general form given above, being given by: The difference from the general form happens because the downvalley path is not perfectly straight. Partial Differential Equations presents a balanced and comprehensive introduction to the concepts and techniques required to solve problems containing unknown functions of multiple variables. No need to modulo 360. Now, you’re probably wondering what circles and triangles have to do with one another and that’s a great question! The text has been developed to meet the scope and sequence of most university physics courses and provides a foundation for a career in mathematics, science, or engineering.

Copyright © 2003-2021 TechOnTheNet.com. The \(\sin{\frac{2\pi }{3}}=\frac{\sqrt{3}}{2}\), because it hits at the point\((-\frac{1}{2},\frac{\sqrt{3}}{2})\). For instance, if our given angle is –110°, then we would add it to 360° to find our positive angle of 250° (–110° + 360° = 250°). What is its angular speed in rad/s? This book takes a cyber-physical approach to embedded systems, introducing the engineering concepts underlying embedded systems as a technology and as a subject of study. Found inside – Page 325Bus voltage versus time for paralleling one loaded alternator with three loaded machines at 210 degrees . ... The single output from the constantspeed drive is alternator speed or angular velocity w , in radians per second . Since we are told that the value of Ɵ is in the first quadrant and we know that the y-coordinate of a point on the unit circle represents sine, we can look for a point on the unit circle where the y-coordinate is \(\frac{1}{2}\). 2) 210 + 210 = 420. I hope this review was helpful. Nevertheless, it is possible to see a very strong sinuosity in the succession of few river bends, or of laces on some mountain roads. m Y tA]lxlt nrAiXgShztMsG vrJeWsNesrWvDerdW. In a right triangle, however, one of the angles is already known: the right angle, or the #90^o# angle.. Let the other two angles be #x# and #y# (which will be acute).. How can I do this? The ROUND function can be used in VBA code in Microsoft Excel. The only point in the first quadrant with y-coordinate \(\frac{1}{2}\) is the point that represents angle 30° which is \(\frac{π}{6}\) in radians. Now in its third edition, Mathematical Concepts in the Physical Sciences provides a comprehensive introduction to the areas of mathematical physics. It combines all the essential math concepts into one compact, clearly written reference.

The number of additions is 1. It can be used as a VBA function (VBA) in Excel. Applying these conditions, we can say that, Let this guide show you the easy way to tackle algebra. You'll get plain-English explanations of the basics — and the tougher stuff — with examples you can understand. The sinuosity index can be explained, then, as the deviations from a path defined by the direction of maximum downslope. All rights reserved. With a radius of one, that wouldn’t be very difficult. A reference angle is the acute version of any angle determined by repeatedly subtracting or adding straight angle (1 / 2 turn, 180°, or π radians), to the results as necessary, until the magnitude of the result is an acute angle, a value between 0 and 1 / 4 turn, 90°, or π / 2 radians. The \(\text{sin }Ɵ=\frac{1}{2}\), where 0° < Ɵ < 90°. Found inside – Page 299270 ' or 3/2 radians 240 ' or 4 / 3x radians 300 or 5/3 radians 210 or Polar Coordinate and Polar Graph and Polar Scale ... The values of the radians are many times expressed in terms of a constant number called pi ( designated by the ... If we look closely at our circle, we can actually find right triangles in it. The sinuosity value is really significant when the line is continuously differentiable (no angular point). Found inside – Page 336They are read as 'pi by three 7 , 'pi by four', etc. ... Leave all radian results in terms of n: Degrees 30 45 60 90 120 150 180 1 a z 15 31 Radians 6 4 3 2 4 7r Degrees 210 240 270 315 360 211 2 t1: Radians 4 3 6 21: 4. The R Book is aimed at undergraduates, postgraduates andprofessionals in science, engineering and medicine. It is alsoideal for students and professionals in statistics, economics,geography and the social sciences. For rivers, the conventional classes of sinuosity, SI, are: It has been claimed that river shapes are governed by a self-organizing system that causes their average sinuosity (measured in terms of the source-to-mouth distance, not channel length) to be π,[3] but this has not been borne out by later studies, which found an average value less than 2. An important thing to note when discussing these angle measures is that the angles must be in standard position. We will look for the coordinates where the ratio of \(\frac{y}{x}=\frac{\sqrt{3}}{3}\). This can be solved by multiplying \(\frac{5π}{3}\) by the conversion factor \(\)\frac{180\text{ degrees}}{π}. Note: The trig functions work in radians.

org. Subaru's EZ30D was a 3.0-litre horizontally-opposed (or 'boxer') six-cylinder petrol engine. Alternating Current Fundamentals - Page 20 Terms in this set (158) ... Use pi/180 to convert degrees to radians Answer: .57 rads. First radian value is the approximately calculated with pi (π) and the second radian value is the exact radian value in terms of pi (π). One of the most common uses of trigonometry is in finding the measures of an angle given two sides of a right triangle. What is the value of Ɵ in radians? Personal Computing - Volume 1 - Page 124 Question: I read your explanation of how the ROUND function works in VBA using the round-to-even logic. Make Your Own Miniature Electric Hub Motor : 14 Steps ... .). This Excel tutorial explains how to use the Excel ROUND function (in VBA) with syntax and examples. Unit Circle Freeman and Co., 522p. .. Here is an example: We know the radius is 1 and we can use SOHCAHTOA to find that the opposite is \(\frac{1}{2}\) and the adjacent side is \(\sqrt{3}\). Found inside – Page 912 In the work that follows , we shall use both the radian and the degree as units of angular measure . If at any time an angle is given in terms of radians and an approximation to the nearest second is acceptable , we may use 1 radian ... (Simplify your answer. The book is often used by commercial operators as part of their induction or transition training on the C210. "This book by Lisa Tauxe and others is a marvelous tool for education and research in Paleomagnetism. Algebra I For Dummies Found inside – Page 192For example , the inverse tangent of 1 is 45 degrees or , equivalently , a / 4 radians . ... purposes of calculating pi , however , is the fact that an inverse trigonometric function can be " expanded ” as a series , the terms of which ... For example: Sin(30/Deg) will return 0.5, and ATan(1)*Deg will return 45. Leopold, Luna B., Wolman, M.G., and Miller, J.P., 1964, Fluvial Processes in Geomorphology, San Francisco, W.H. Solving Right Triangles - Trigonometry | Socratic Cessna 210 Training Manual The \(\cos{180^{\circ}}=-1\), because at \(180°\), the ray hits the circle at the point \((-1,0)\). As a reminder, the ROUND function uses something commonly referred to as bankers rounding. If an angle is not in standard position, it is important to place it in standard position before using the points to find your trig values. Most angles on your circle will be a fraction of pi. Here are the radian measurements for the first quadrant: 0 degree angles have a measurement of 0. We can solve this by multiplying 180 degrees by the conversion factor \(\frac{π\text{ rad}}{180\text{ degrees}}\). . Step 1: Use pi/180 to convert degrees into rads ... A compact disk rotates at 210 revolutions per minute. Angle conversion helps you to calculate degrees and radians with value pi. Found inside – Page 16200 210 220 230 0.5 PENCIL ALLOWANCE SQUARE CENTAGON 8 10 12 HEXAGON RALLELOGRAM ISOMETRIC LINES 一致。 UNEAR RADIAN ... 7.95 ( tax ex ) " no fuss ” reflex angles . angles in terms of pi , and for marking out giant polyhedra nets . Academia.edu is a platform for academics to share research papers. If you want to avoid bankers rounding, you can create your own custom function as follows: And then call the StandardRound function instead of using the Round function. The Microsoft Excel ROUND function returns a number rounded to a specified number of digits. The tangent of which two angles is \(\frac{\sqrt{3}}{3}\)? Here are some examples of what the ROUND function would return: In this example, the variable called LNumber would now contain the value of 210.7. Home | About Us | Contact Us | Testimonials | Donate. If you need to find the tangent value, simply put sine over cosine, or the \(y\)-coordinate over the \(x\)-coordinate. What has been lacking, however, is a comprehensive reference for foundation engineers that incorporates these state-of-the-art concepts and techniques. The Foundation Engineering Handbook fills that void. Let's say the wheel is revolving n times per minute. To define our trigonometric functions, we begin by drawing a unit circle, a circle centered at the origin with radius 1, as shown in Figure 2.

Found inside – Page 124As an extended option , use ASIN and Acos ; for degrees instead of radians use SIND , COSD , TAND , ASIND , ACOŚD and ATAND ; for logarithms base 10 use LOGTEN ; and for multiplying an argument by pi use PI . instead of physically ... \(-\frac{\sqrt{2}}{2}\div-\frac{\sqrt{2}}{2}=1\), so tan \(\frac{5π}{4}=1\). Trigonometry is the study of how a triangle’s sides and angles relate to one another. Measuring in radians relates the angle to \(\pi \), so \(\pi \) will be in almost every angle measure when measuring in radians. This text is written for undergraduates who are studying orbital mechanics for the first time and have completed courses in physics, dynamics, and mathematics, including differential equations and applied linear algebra.

This unique book is written so both undergraduate and graduate readers can easily comprehend the content without the usual prerequisites, such as structural analysis. This simplifies to 300 degrees.

Step 1: Convert rpm … CK-12's Trigonometry-Second Edition is a clear presentation of trigonometry for the high school student. The value of sin 120 degrees in decimal is 0.866025403. . for the central axis of the small intestine), although it is often performed in a plane (with then a possible orthogonal projection of the curve in the selected plan; "classic" sinuosity on the horizontal plane, longitudinal profile sinuosity on the vertical plane).
For degrees, multiply or divide by the Deg variable. 16 units. Resource added for the Mathematics 108041 courses. In this book, the reader is expected to do more than read the book but is expected to study the material in the book by working out examples rather than just reading about them. A band brake is installed on a drum rotating at a 250 rpm, and a diameter of 900 mm. For Australia, the EZ30D engine was solely available on the Subaru BH Outback from 2000-03. Written by the lead p5.js developer and the founders of Processing, this book provides an introduction to the creative possibilities of today's Web, using JavaScript and HTML. Think of radians and degrees like centimeters and inches. We know that the x– and y-coordinates of the points on the unit circle represent cosine and sine of the angle, respectively. But today we are going to look at this circle through the lens of trigonometry. Describes the LISP programming language, and covers basic procedures, data, and modularity. What is the value of sin \(\frac{3π}{4}\)? Excel for Office 365, Excel 2019, Excel 2016, Excel 2013, Excel 2011 for Mac, Excel 2010, Excel 2007, Excel 2003, Excel XP, Excel 2000. Before we get into the unit circle itself, let’s talk about degrees and radians. The coordinate points where the measure of a specific angle hits the circle gives us our sine and cosine values. We then use our unit circle, with angles in standard position, to find the trig values of common angle measurements. Locate \(\frac{4π}{3}\), which is equivalent to 240° at the coordinate \((-\frac{1}{2},-\frac{\sqrt{3}}{2})\). Going back to our example of \(60°\), \(\sin{60^{\circ}}=\frac{\sqrt{3}}{2}\), our \(y\)-coordinate, \(\cos{60^{\circ}}=\frac{1}{2}\), our \(x\)-coordinate, and \(\tan{60^{\circ}}=\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\), which simplifies to \(\sqrt{3}\). A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples. But there’s actually another way you can measure an angle, and that’s by measuring in radians. This text provides a brief review of the principles of dynamics so that terminology and notation are consistent and applies these principles to derive mathematical models of dynamic mechanical systems. Convert 60 degrees to radians. This article explains what a reference angle is, providing a reference angle definition. The tangent of an angle is the ratio of \(\frac{\text{sin}}{\text{cos}}\). Online calculator for cos -1 (x) Note. Solve the right triangle ABC, with C = 90 degrees, A = 23.6 degrees, and c = 3.42 cm. The source below can be used to create translated or updated versions of this file. Now let’s try an example converting from radians to degrees. Length of arc = S = r θ = 9 x (5π/6) = 7. hope it helps Trigonometry 7th Edition answers to Chapter 3 - Section 3. find the area of sector abc. See www.grantadesign.com for information NEW TO THIS EDITION: Text and figures have been revised and updated throughout The number of worked examples has been increased by 50% The number of standard end-of-chapter exercises in the text has ... The radians of a unit circle go from 0 to 2𝛑. Since \(\pi \) is the ratio of a circle’s circumference to its diameter, it makes sense that we use radians most often when working with circles. Designed to encourage a clear understanding of the nature and design of planar mechanisms, this book favours a frank and straightforward approach to teaching the basics of planar mechanism design and the theory of machines with fully worked ... The tangent function is found by dividing the y-value by the x-value. Begin at 0 degrees, the position of sensor A. For instance, a right angle has 90 degrees, a straight angle has 180 degrees, and there’s an angle for every number in between. We know that the x-coordinates of a point on the unit circle represent cosine. Academia.edu is a platform for academics to share research papers. The sum of the measures of all the angles in a triangle is always equal to #180^o#.. As most of you have heard before, a circle has 360 degrees. In this video, we will go over what the unit circle is and what it is used for. This may seem fairly common and you might be getting excited if you think I’m going to ask you to find the circumference or area. Newtonian mechanics : dynamics of a point mass (1001-1108) - Dynamics of a system of point masses (1109-1144) - Dynamics of rigid bodies (1145-1223) - Dynamics of deformable bodies (1224-1272) - Analytical mechanics : Lagrange's equations ... Please re-enable javascript in your browser settings. The calculation of the sinuosity is valid in a 3-dimensional space (e.g. The Microsoft Excel ROUND function returns a number rounded to a specified number of digits. Finding Function Values for the Sine and Cosine. Note: The factorial function is implemented for all real numbers -- integers or non-integers, positive, or negative. English: Wikipedia’s list of 188 cognitive biases, grouped into categories and rendered by John Manoogian III (jm3) as a radial dendrogram (circle diagram).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°) ⇒ 120 degrees = 120° × (π/180°) rad = … We’re going to take our \(270°\) and multiply by our conversion factor, which is \(\frac{\pi \text{ rad}}{180^{\circ}}\). Think of radians and degrees like centimeters and inches. It also has \(2\pi \) radians. sinhala wela katha wal katha sinhala wela new sinhala wela teacher wal katha new sinhala wal video wela katha sinhala wela pdf sinhala wal katha wala. Description. Sinuosity, sinuosity index, or sinuosity coefficient of a continuously differentiable curve having at least one inflection point is the ratio of the curvilinear length (along the curve) and the Euclidean distance (straight line) between the end points of the curve. Remember, you can convert between radians and degrees using the conversion, \(\pi \text{ rad}=180^{\circ}\). The coverage of the book is quite broad and includes free and forced vibrations of 1-degree-of-freedom, multi-degree-of-freedom, and continuous systems. Use the Unit Circle. CK-12 Foundation's Math Analysis FlexBook is a rigorous text that takes students from analyzing functions to mathematical induction to an introduction to calculus. This 4th S.I. ed. covers all of the standard topics of mechanics of materials in a clear and readable style which makes even difficult subjects accessible to the student. Let’s look at \(\frac{\pi }{6}\text{ rad}\). So before using this function, please read the following: The ROUND function utilizes round-to-even logic. For example, with a ray coming from the angle \(60°\), the point that ray hits the unit circle is at \((\frac{1}{2},\frac{\sqrt{3}}{2})\). Each slot is 210 electrical degrees, so start adding. View Answer The CEILING function is a built-in function in Excel that is categorized as a Math/Trig Function.It can be used as a worksheet function (WS) in Excel. The distance between both ends can also be evaluated by a plurality of segments according to a broken line passing through the successive inflection points (sinuosity of order 2). In a pair of coordinates \((x,y)\) on the unit circle, the coordinate x is the cosine of the angle formed by the point, the origin, and the x-axis. The classification of a sinuosity (e.g. Use the Unit Circle. This …
As most of you have heard before, a circle has 360 degrees. Found inside – Page 210In P , write the polynomial 4x2 – x + 5 in terms of the basis polynomials 1 , 1- x ( 1 – x ) ?, ( 1 – x ) ' . ... the x- and y - axes in the plane are rotated counterclockwise through an angle of 0 ( measured in degrees or radians ) . This updated edition features additional material on the creation of visual stimuli, advanced psychophysics, analysis of LFP data, choice probabilities, synchrony, and advanced spectral analysis. And the 0.000001 does not significantly affect the value of your expression so you shouldn't introduce any calculation errors. The syntax for the ROUND function in Microsoft Excel is: The ROUND function returns a numeric value. Radians is always represented in terms of pi, where the value of pi is equal to 22/7 or 3.14. Then we can discuss circular motion in terms of the coordinate pairs. Found inside – Page 63This dot separation is then converted in line 210 ( by multiplying by Pl and dividing by 180 ) to form the STEP for the FOR NEXT loop in line ... As we know , 2 PI radians equal 360 degrees , and hence the statement in line 230. Let’s say we want to convert \(270°\) to radians. That is: 1) 0 + 210 = 210.

The unit circle is a collection of the most common right triangles, so we use it to remember the trig values of the most common angles. In these cases, the last digit after rounding is always an even number. We believe you can perform better on your exam, so we work hard to provide you with the best study guides, practice questions, and flashcards to empower you to be your best. If we multiply this by our conversion factor, we’re going to multiply this time by \(\frac{180^{\circ}}{\pi \text{ rad}}\), which then simplifies to \(30°\). If the expression that you are rounding ends with a 5, the ROUND function will round the expression so that the last digit is an even number. A radian is the measure of an angle. Please read our ROUND function (WS) page if you are looking for the worksheet version of the ROUND function as it has a very different syntax. Keep in mind that in this equation "latMid" is in radians while "m_per_deg_lat" is for degrees. Most of the time, when you measure an angle, you measure it in degrees. ): the sinuosity of the same curved line could be considered very strong for a high speed train but low for a river. Determine the time when the potential energy is twice the kinetic energy. Subtract 360. Answer: You could always use the following logic: If you wanted to round 12.65 to 1 decimal place in the traditional sense (where 12.65 rounded to 1 decimal place is 12.7, instead of 12.6), try adding 0.000001 to your number before applying the ROUND function: By adding the 0.000001, the expression that you are rounding will end in 1, instead of 5...causing the ROUND function to round in the traditional way. The motion of a 200 g particle is described by x(t) = 5.0 cm cos (50 pi t + (pi/3)) with x in cm and t in seconds. The other ray of the angle is placed at the angle measure formed by traveling counter-clockwise along the circle. Found inside – Page 210EMPTY TYPE 2503 FORMAT ( 1X , ' Number of series terms ( < or = 14 ) = ' $ ) ACCEPT * , NIT TYPE 2504 FORMAT ( 1X , ' Enter radius ... Degrees ' , PI = 4.DØ * DA " AN ( 1.DO ) CONVER ? ANGLES TO RADIANS DECA = TE A / 180 . DO * PI ETA ... However, I really need to round some values in the traditional sense (where 5 always rounds up). Coterminal Calculator Radians To find an angle coterminal to another you can do so by simply adding or subtracting any multiple of 360 degrees or 2 pi radians. What is the value of cos 90° ? If you’re a scientist who programs with Python, this practical guide not only teaches you the fundamental parts of SciPy and libraries related to it, but also gives you a taste for beautiful, easy-to-read code that you can use in practice ... Convert radians to degrees (rad to degree). For non-integers its accuracy is about 6 significant figures.

CK-12 Foundation's Single Variable Calculus FlexBook introduces high school students to the topics covered in the Calculus AB course. Topics include: Limits, Derivatives, and Integration. The curve must be continuous (no jump) between the two ends. Do not include the degree symbol in your answer. One of the goals of this book is to prepare you for a course in calculus by directing your attention away from particular values of a function to a study of the function as an object in itself.

So if you want to compute this for a latitude of 30N (say), in the equation latMid = pi*30/180 . Perplexed by polynomials? Don’t worry! This friendly guide takes the torture out of trigonometry by explaining everything in plain English, offering lots of easy-to-grasp examples, and adding a dash of humor and fun. For this reason, bedrock streams that flow directly downslope have a sinuosity index of 1, and meandering streams have a sinuosity index that is greater than 1.[2]. Thanks for watching and happy studying! They are two different forms of measurement but they can be used to measure the same thing and can be converted between. In a pair of coordinates \((x,y)\) on the unit circle, the coordinate y is the sine of the angle formed by the point, the origin, and the x-axis. ly/34WIWmZ t Arc Length & Sector Area Name: Date: 1. Keep track of the number of times you add, wrapping around 360 degrees for each result, until the result is equal to 120. Found inside – Page 5510.7635 TT 11. 137 ° 26 ' 12. 145o = 0.8056 ñ 13. Express as some number times pi . 120 ° 2 TT 120 ° 180 ° 7 TT 3 | TT 210 ° = 6 ITT 30 ° 6 51T - 60 ° - 150 ° = ܘܐ 3 II † 18 13T 12 14. Express z radians in degrees . Solution : ti. The ROUND function is a built-in function in Excel that is categorized as a Math/Trig Function.It can be used as a VBA function (VBA) in Excel. A unit circle is a circle which has a radius of one unit and its center is at the origin. box, make sure degrees is on and then click on the Find button) and if we ask the Calculator to find approximations it finds the sequence with legs differing by one that we found above. The \(x\)-coordinate gives us our cosine value for that angle, and the \(y\)-coordinate gives us our sine value. While using this site, you agree to have read and accepted our Terms of Service and Privacy Policy. It is also possible to distinguish the case where the stream flowing on the line could not physically travel the distance between the ends: in some hydraulic studies, this leads to assign a sinuosity value of 1 for a torrent flowing over rocky bedrock along a horizontal rectilinear projection, even if the slope angle varies. This text assumes students have been exposed to intermediate algebra, and it focuses on the applications of statistical knowledge rather than the theory behind it. "A meandering tale: the truth about pi and rivers", List of rivers that have reversed direction, https://en.wikipedia.org/w/index.php?title=Sinuosity&oldid=1052063987, Short description is different from Wikidata, Creative Commons Attribution-ShareAlike License, 2 inverted continuous semicircles located in the same plane is, This page was last edited on 27 October 2021, at 04:59. So, be sure to only use the ROUND function if this is your desired result. Learn how to calculate radian to degree. This then simplifies to \(\frac{3\pi }{2}\text { rad}\). ... (1 / 57.2958) radians 1 degree = 0.01745329 rad (approximately) in terms of π radians = degrees × 180 / π 1 degree = (π / 180) rad Degrees to Radians Values. Coterminal angles. What is the value of tan \(\frac{5π}{4}\)?

... Radian to degree two decimals in terms of pi. This is the second edition of Travis Oliphant's A Guide to NumPy originally published electronically in 2006. Quickly Engages in Applying Algorithmic Techniques to Solve Practical Signal Processing Problems With its active, hands-on learning approach, this text enables readers to master the underlying principles of digital signal processing and its ... strong / weak) often depends on the cartographic scale of the curve (see the coastline paradox for further details) and of the object velocity which flowing therethrough (river, avalanche, car, bicycle, bobsleigh, skier, high speed train, etc. For now, we will put it on the screen so you can refer back to it, but eventually, you may want to memorize it since these values come up frequently in mathematics. by Mometrix Test Preparation | Last Updated: November 15, 2021. Since \(\pi \) is the ratio of a circle’s circumference to its diameter, it makes sense that we use radians most often when working with circles. The x-coordinate of the point is \(-\frac{1}{2}\) and the cosine of \(\frac{4π}{3}\). Radians to Degrees conversion calculator. With this handbook, you’ll learn how to use: IPython and Jupyter: provide computational environments for data scientists using Python NumPy: includes the ndarray for efficient storage and manipulation of dense data arrays in Python Pandas ... Sin 120 degrees can also be expressed using the equivalent of the given angle (120 degrees) in radians (2.09439 . Category model by Buster Benson, biases linked to corresponding Wikipedia articles by TilmannR. The x– and y-coordinates for the angles 30° and 210° simplify to \(\frac{\sqrt{3}}{3}\). This simplifies to π rad. – Eli Holmes Online calculator for quick calculations, along with a large collection of calculators on math, finance, fitness, and more, each with related in-depth information. In Excel's VBA environment, the ROUND function returns a number rounded to a specified number of decimal places. The Microsoft Excel CEILING function returns a number rounded up based on a multiple of significance. Answer (1 of 10): Rpm is just a measure of how many times a wheel is revolving per minute. It is very important to note that the VBA ROUND function behaves a little peculiar and uses something commonly referred to as bankers rounding. This dimensionless quantity can also be rephrased as the "actual path length" divided by the "shortest path length" of a curve. And \(\frac{\sqrt{2}}{\sqrt{2}}=1\). [4], Ratio of arc length and straight-line distance between two points on a wave-like function. Standard position simply means that the vertex of the angle is at the origin of the circle and that one ray of the angle is on the positive \(x\)-axis. The ROUND function is a built-in function in Excel that is categorized as a Math/Trig Function. And the \(\tan{\frac{\pi }{4}}=1\) because the ray hits the circle at the point \((\sqrt{2},\sqrt{2})\).

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