What is Radians: Definition and 110 Discussions

The radian, denoted by the symbol




rad



{\displaystyle {\text{rad}}}
, is the SI unit for measuring angles, and is the standard unit of angular measure used in many areas of mathematics. The unit was formerly an SI supplementary unit (before that category was abolished in 1995) and the radian is now an SI derived unit. The radian is defined in the SI as being a dimensionless value, and its symbol is accordingly often omitted, especially in mathematical writing.

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  1. M

    Finding cos in radians without calculator? Help?

    Hey guys this question is going to sound pretty dumb, but I never learned how to do this. What if I want to find say, cos(pi/5) but I don't have a calculator? Even if I did have a calculator, I want it in nice values, like square roots, rather than decimals anyway. If I have something...
  2. karush

    MHB Online calculators that have radians on the x axis

    just curious if anyone knows where there is online graphing program that will graph trig function with radians on the x axis tried Wolfframapha but not thanks ahead
  3. C

    MHB Misunderstanding between converting radians and degrees

    OK I have a right angled triangle and one angle is 1/8 pi. So I know two angles then, 90 degrees and 1/8 pi. I also know the hypotenuse has a length 5 units. I am required to find the angle remaining in radians. The problem I have is that although I can do conversions on the calculator they...
  4. A

    Angles - why in radians instead of in degrees?

    angles -- why in radians instead of in degrees? greetings, why all the angle in electrical is represented in radian instead in degree? advanced thanks
  5. M

    A flywheel makes 80 radians in 4 second and is rotating with constant angular acceler

    A flywheel makes 80 radians in 4 second and is rotating with constant angular acceleration during this time . It makes 60 radians in next 4 second with constant angular velocity . Find initial angular velocity and the angular acceleration ? my answer is form this equation Q= w0t +...
  6. phosgene

    Finding k such that u and v form {\pi}/3 Radians

    Homework Statement Let u = (1,k) and v = (3,4). Find k such that the angle between u and v is {\pi}/3 radians. Homework Equations u{\bullet}v=||u|| ||v|| cos{\theta}=x_{1}x_{2}+y_{1}y_{2} ||u||=\sqrt{x^2 + y^2} The Attempt at a Solution Firstly I calculate the length of v and...
  7. F

    Piecewise function radians and numbers ?

    Hello, I have encountered the following piecewise function: (x − 1)^2 if x > 1 tan x if −π/2 < x ≤ 0 How would I interpret/graph this, as it seems to be referring to radians and regular numbers ? Thanks for any help.
  8. C

    Revolutions of a tire and angle in radians thru warranty

    Homework Statement The tires on a new car have a radius of .275 meters and are warranted for 75,000km a)what is the angle in radians that one of these tires will rotate thru in the warranty period? b) how many revolutions does this make?Homework Equations 1rev = 2pi radians circumference =...
  9. S

    Efficiently Calculate Radian Circles | Part B Explanation

    for part b I'm not sure how to do it any hints on how to do it? I've tried using sine rule etc but I'm just guessing, and I'm pretty sure there is a more simple method.
  10. N

    Why do radians *work* in calculus and higher maths?

    Hello, I searched the forum and couldn't find this topic, so I'll try and describe my question. I want to know why using radians work and while they are 'natural'. I think the key equation is... lim x→0 (sin x) / x = 1 ...because it makes the derivatives of trigonometric functions...
  11. C

    Working with degrees instead of radians

    Homework Statement If x is measured in radians, then the derivative of Sin[x] with respect to x is Cos[x]. Use the formula Sin [x degrees] = Sin [2π/360 x radians] to calculate the derivative of Sin [x degrees] with respect to x. Why does the resulting formula make calculus difficult...
  12. nomadreid

    Why does Euler's identity work only in Radians?

    e^iA = cosA + i*sinA is true iff A is expressed in Radians. Why that particular unit? (I'm not sure this rubric is the right one for this question, but since it didn't seem to fit any of the other rubrics, I put it here.)
  13. N

    Why we measure angles with Radians

    Hi guys, I had been wondering for a while why it is that we use the radian as the unit of angular measurement in higher sciences and mathematics (calculus, physics, engineering) as opposed to the degree. In reviewing the relationship between the degree and radian, I believe that I have...
  14. L

    Angular displacement in radians

    Homework Statement The radius of a wheel is 0.450 m. A rope is wound around the outer rim of the wheel. The rope is pulled with a force of magnitude 4.64 N, unwinding the rope and making the wheel spin CCW about its central axis. Ignore the mass of the rope. What is the angular...
  15. 1

    Rhyme and Reason Behind Radians?

    Preface: This question is a result of personal interest, and has nothing to do with any assignment. Okay here's the deal; I've tutored trig in the past, and I've noticed one thing that a lot of folks have trouble with is the fact that there are two pi radians per circle. (It doesn't help that...
  16. N

    Angular velocity and those damn radians

    I don't get radians. I understand it's a constant, ie: circumference/radius = 2pi because 2*r*pi equals circumference BUt I don't get why it is so damn handy for measuring angles! THe formula for angular velocity is \omega*r=(2pi/t)*r where omega=change in angle divided by time. what the...
  17. J

    Expressing a decimal number in radians in terms of pi in a fraction

    Homework Statement arctan(sin((3 / 4) * pi) * 2) = 0.955316618 I want to express that in terms of a fraction with reference to pi. The Attempt at a Solution I thought of first dividing that by pi itself, and then convert the resulting number into a fraction and tack pi on at the...
  18. G

    Help With Radians Conversions (sort of)

    Homework Statement Hey So I have to create a list from 0 to 2 pi in increments of .1 radian. I realized that I had no idea how to do this. It's clear based on what's asked of me that the values in between 0 and 2 pi should be in radians sense the end values are 0 and 2 pi. I know that...
  19. T

    Converting cosine(.9812) to radians two answers

    Homework Statement how would you write cosine(.9812) in two ways expressed with radians (calculator based) Homework Equations cos-1(x) The Attempt at a Solution i just plugged cos-1(.9812) and got .1942 radians. If this is one of the answers how do i find the other.
  20. C

    Converting Degrees to Radians: A Quick Guide

    I know that 65° = pi/180 = 13pi / 36. But when I divide 65 / 180° I get. 3261. How would I convert this into 13pi/36 ? I know I am forgetting the basics..
  21. M

    Unit Circle: 360 Degrees = 2(pi) Radians

    The book talks about a unit circle... 360 deg = 2(pi) rad if it wasnt a unit circle... say r = 4 would it then be 360 deg = 8(pi) rad?
  22. T

    'New' type of angle measurement to often replace radians

    Maybe I'm biased because of the kind of projects I'm pursuing (raytracing), but I can't help feeling that for many areas, instead of defining a circle in terms of radians (or degrees for that matter), we should simply use unity and define say, a quarter of a circle as being 0.25. Obviously a...
  23. S

    What is the Simple Explanation for Radians and Trigonometric Functions?

    Im currently in Calc II and am finding myself totally lost when it comes to solving things like sin(pi/3) and trig of that nature. I am very reliant on my calculator and am extremely fond of degrees, but I NEED to be able to find the definite integral of cos(x) from 0 to (pi/3) and problems that...
  24. S

    Finding the exact value for period in radians

    Homework Statement What is the exact period of the function f(x)= 6 sin (4x+pi) = a sin (b) Homework Equations Period= 2pi/(abs b) The Attempt at a Solution I found the period as 2pi/(4+pi), this is said to be no the...
  25. S

    Converting degrees to radians (in relation to pie)

    Homework Statement convert 38 degrees to radians. Give the exact answer in the form of pie. Homework Equations 180 degrees=pie The Attempt at a Solution not sure how to convert degrees to radians can anyone help??
  26. M

    Writing decimal radians in terms of Pi

    Hello :smile: Sorry if this is in the wrong place, I don't know where else to put it. Is there a way to write radians as decimals in terms of Pi? I'm currently doing Polar Coordinates with Argand Diagrams, and this is something I'm curious about. I've just done a question and come...
  27. R

    Need help understanding Fourier transform in Hz vs radians

    Hi guys, I'm having some issues understanding something about the Fourier transform. In my first signals and systems class we used the angular frequency omega. Doing it like that you end up with a weighing factor or 1/(2pi) when you take the transform. Now in the dsp class I am taking now we...
  28. T

    Converting angles in to degree to angles in radians

    Homework Statement Convert the following angles in degree to angles in radians: 15° 60° 80° Homework Equations Now i know that 2 ti c = 360° And that 6.28 c = 360° The Attempt at a Solution I just can't quite get my head around it, what calculation should...
  29. R

    Calculating Solid Angle from Light Source: Steradians to Radians?

    I have a light source emitting near a surface and then getting refracted. I have calculated the solid angle leaving the surface of the light I am interested in but need to find what cone this corresponds to from the emitter. Can I just stick half the solid angle into Snell's law equation even...
  30. C

    Find its angular acceleration in radians per second per second

    A potter's wheel moves uniformly from rest to an angular speed of 0.23 rev/s in 29 s.
  31. F

    Convert 75 Degrees to Radian Measure - 5/12 pi

    convert 75 degrees to radian measure the answer is 5/12 pi i know that for converting degrees to radians you multiply the degrees by pi/180 degrees and when i do it i get the answer 1.3089... but how do you get the answer as above, in that form? i have changed the mode of my calculator...
  32. U

    Calculating the Radius of a Rotating Wheel Using Radians and Arc Length

    Homework Statement When a wheel is rotated through an angle of 35o, a point on the circumference travels through an arc length of 2.5m. When the wheel is rotated through angles of 35 radians and 35 revolutions, the same point travels through arc lengths of 143m and 9.0 x 102m, respectively...
  33. O

    Radians to Meters: Conversion & Possibilities

    How do you convert radians to meters?? Is it even possible?
  34. O

    Converting Radians to Vector Notation for Simplifying Expressions

    The arc length of a circle is radius times the angle between the two radius legs that connect the arc. Thus dL = R d@ and dF = I dL x B where B and dL and dF are vectors. how can I convert dL = R d@ into vector notation so that I can simplify these two expressions??
  35. P

    Find Radians: How to Use Sin to Solve for X

    I do not need you to give me an answer just a formula I have some problems to work and I cannot find anything through searching, I can make up a problem, but for example find sin3x if sinx=1/3 and 0 < or equal to sin greater than or equal to pie/2 How would I find x? I now how to...
  36. B

    Angular displacement in radians problem

    Homework Statement what is the angular displacement after 45 second if a wheel spins at 46.07669 radians/s Homework Equations The Attempt at a Solution i got 2073.45105 and i don't know why that is not right
  37. S

    Rotate a graph by a given number of radians?

    Is there a way to rotate a graph by a given number of radians? for example, take to standard parabola where the directrix is a horizontal or vertical line, and make it a line of any slope?
  38. B

    Finding Angle Between Vectors Using Arc Length and Radius

    Homework Statement quick question...im given the arc length ( 1m ) and the radius ( 1.5m )...to find the angle between the two vectors...do i just plug into angle=S/R? Homework Equations angle = S / R The Attempt at a Solution 1/1.5= 0.67
  39. Q

    Identify Quadrant of Angle (radians)

    Homework Statement Determine the quadrant in which the terminal side of the angle lies. (The angle is given in radians.) a) -1 b) -2 The Attempt at a Solution a) -1 * (180/3.14) = -57.3 degrees -- Quadrant IV b) -2 * (180/3.14) = -114.6 degrees -- Quadrant III - Is...
  40. R

    Another angular acceleration problem. Converting radians to meters

    [SOLVED] Another angular acceleration problem. Converting radians to meters... Homework Statement A gyroscope flywheel of radius 3.13 cm is accelerated from rest at 15.0 rad/s2 until its angular speed is 2760 rev/min. (a) What is the tangential acceleration of a point on the rim of the...
  41. D

    Area Common to 2 Circles: Radians Question

    "two circles of radii 5cm and 12cm are drawn, partly overlapping. Their centres are 13cm apart. Find the area common to the 2 circles" I'm not quite sure how to do this. I think I am meant to be using the area of sector as if I draw a line down the middle of the area formed I can use the...
  42. R

    Proving area with radians

    in a circle with perimeter of 20cm a sector has radius r, angle θ radians and area Acm^2 prove that A= 25-(r-5)^2 A=1/2 r^2 θ c=2Πr the only thing that I can think to do is c=2Πr therefore 20=2Πr 10=Πr r=10/Π so then A=1/2 r^2 θ =1/2 (10/Π)^2 θ = θ (100/2Π^2)
  43. E

    Solving tan(theta)=2/5 - 2.62 radians

    Homework Statement The tan(theta)=2/5 Homework Equations The Attempt at a Solution I forgot how, I had no clue so I looked in the solutions and it was 2.62 radians, I just don't know how they got that, I am not sure on what to do. Its for trigonometric forms of complex numbers...
  44. L

    Radians vs Degrees: When to Use in Calculus & Physics

    So I have a few different calculators I use. I am currently in a Calculus 1 and Physics 1 course. Both for engineers. As am example of what I am trying to explain, such as my physics HW It asked me to calculate the magnitude of the Vectors A+B+C. I do so and It worked fine, I did this is...
  45. B

    Convert 477 rev/min to Radians: Answer & Explanation

    If I was given 477 rev/min and I need to convert to radians, I would use: 477rev (2*pi radians/1 rev) = 2997.07 radians Question is do I need to divide by 60 to get radians/second instead of minutes?
  46. M

    Trigonometric functions and radians

    Solve the following equation giving values from -\pi to \pi: cos (2v - \frac{\pi}{3}) = \cos v Here is my attempt to solve it. As the cosine of the two is the same, the angles should also be the same leaving 2v - \frac{\pi}{3} = v + 2 \pi n Then if I move the right over to the left, I get...
  47. A

    Radians for Inclined PLane?

    The formula for calculating the force required to move an object (ignoring friction, etc.) up an inclined plane is: F = Mgsinθ Where: F = force (N) Mg = gravity (9.81m/s²) θ = angle of inclination (degrees out of 360, or radians?) The question I have is: what is used to...
  48. B

    Radians - why do we use these instead of decimal?

    I'm basically homeschooled in math so please forgive me if this question seems simple, but I have never been able to find a book that shows how radians are calculated. Through inspection I've sort of determined 45 degrees = pie/4, 60 degrees = pie/3, 90 degrees = pie/2, 180 = pie and so forth...
  49. D

    Converting Degrees to Radians in Excel

    Hello everyone, I need help with converting or changing degrees to radians in Microsoft Excel. Currently I'm writing SIN and COS functions but the default angles are in degrees, not radians. How do I format it to radians?
  50. P

    Finding x in Radians: A Puzzling Problem for Pavadrin

    Hey I have recently been studying for my upcoming exams. I am stuck on the following problem involving radians. Here is the diagram for it. Where PQ = the radius of the circle I need to find x in as a percentage in terms of h My working for this problem is as follows in a circle there is...
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