# What is Radians: Definition and 110 Discussions

The radian, denoted by the symbol

, 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. ### Centripetal Acceleration while Swinging a Stone on a String

So my initial understanding is that it completes 5 revolutions per second. I converted the 5 rev to radians, so each revolution is 2pi. Now since I got angle of rotation I can plug it into the angular velocity formula which is Angular velocity= angle of rotation/ time. However since I don't have...

Question: Where is an angle of 10.5π radians in standard position located? A. On the positive vertical axis B. On the negative vertical axis C. In the second quadrant D. In the fourth quadrant I thought I had to divide 10.50 by 3.14, which I thought yielded 3.34π. Then I subtracted 3.34π...

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4. ### Where are the waves out of phase with each other by π radians?

I know that at the antinodes, the diffrence is pi radians and i got 0.25, 0.75, 1.25, and 1.75. for the position of antinodes. but the answer is x = 0.75 m, 1.25 m. I can use drawing to obtain the answer, but my calculation gives me 0.25, 0.75, 1.25, and 1.75. Where am I doing wrong? Thanks!
5. ### Calculators Which steps with my calculator are needed to obtain result in radians?

Hi PF, hope to be publishing in the right forum <moderator's note: moved to the right forum :smile:> ##\arccos{\dfrac{\sqrt{2}}{2}}\mbox{rad}=\dfrac{\pi}{4}\mbox{rad}## This is a trigonometric true, but I've read the steps in my guideline, and I don't manage. The calculator is a chinese...
6. ### I How many degrees / radians is one full orbit of the Earth?

One day consists of slightly more than 360° of rotation (360.9856°) on it's axis (due to Earth's orbit around the Sun). I imagine that one orbit is also either > or < 360° around the sun, relative to the motion of the sun around some object. Is this true, or is the orbit of the Earth...
7. ### Find the phase difference (in radians)

Homework Statement In a Newton's rings apparatus, find the phase difference (in radians) when an air wedge of 500nm thickness is illuminated with red light (lambda = 640nm). t = 500nm lambda = 640nm radians = degrees × pi / 180° Answer) 13 Homework Equations 2pi x path difference / lambda...
8. ### MHB Write 2.158 radians in terms of Pi

Hello, can someone show me how 2.158 radians can also be written as .687pi? I need to learn how to do this so I can write my answer in terms of pi as opposed to 2.158. Thank you in advance. Yeny
9. ### Amplitude of Wave at 5pi/6 Radians in Cycle, y = Asin(kx-wt)

Homework Statement λ = 3m T = .5 s k= 2π/λ = 2.09 radians/m ω= 2π/T = 12.56 = radians/sec v = ω/k = 6m/sec At π radians with sin wave x = 3m At 5π radians/6, x = 2.48 m t = 2.48m/6m/sec = .41 sec What is y at x,t At t0 x = t = 0 [/B]Homework Equations y = Asin(kx-ωt)[/B]The Attempt at a...
10. ### B Are These Radian Equations Correct?

$$0 = 2π/3$$. $$π/6 =3π/4$$ $$π/4 = 5π/6$$ $$π/3 = π$$ $$π/2 = 3π/2$$ $$2π = 2π$$ $$π/2 + 3π/2 = 4π/2$$ I find this a little confusing but quite wonderful. But, what is it?
11. S

### Why is d(theta)/dt in radians?

This is just a conceptual question I don't understand. I am learning Calculus and rate of changes. There are many times where I have to solve for dθ/dt and whenever I do it the answer comes naturally in radians. Could someone explain to me why this is so?
12. ### Dimensionless Units: SI Reform for Clarity & Precision

The topic has been discussed before at PF, in particular @haruspex's Insight Can angles be assigned a dimension? Nature has now published an editorial on the subject: SI units need reform to avoid confusion
13. ### MHB Radians to Degrees, Minutes, Seconds

Reduce the following numbers of radians to degrees, minutes, and seconds. (a). 0.47623. (b). 0.25412. Can someone work out (a) in steps? I can then use it as a guide to solve (b).
14. ### MHB Minutes, Degrees, Seconds to Radians

Express the following angle in radians. 12 degrees, 28 minutes, 4 seconds that is, 12° 28' 4". I cannot apply pi/180° to this problem.
15. ### MHB How can you express an angle in radians without using pi/180°?

Express the following angle in radians. 12 degrees, 28 minutes, that is, 12° 28'. I cannot apply pi/180° to this problem.
16. ### Tips on finding LCM in radians?

Homework Statement Lets say I want to find the LCM of -5π/3 and π/2; Also let's say these points are on the Unit Circle. Homework Equations It's easier to convert to degrees then back to radians but I don't want do that anymore because it's tedious The Attempt at a Solution Thoughts?
17. ### B Radians vs Degrees: Math Trigonometry Explained

Im teaching math and one of my students asked me something about trigonometry. Say you are to generally solve: sin(x + 1) = 0.5 And that's all the information you are given. How would you know to solve for radians or degrees?
18. ### B Why I think radians should *not* be dimensionless

As most know and rest can find out, radians are a dimensionless unit. Actually, it's even worse: angle in general is a dimensionless quantity. That stems from it being defined as a ratio of the arc versus the radius. I now present my opinion of disagreement to this concept. In the strict...
19. ### Find Solutions to Tan x = Cos x in Radians

Homework Statement Find all numbers x ∈ [0, 2π] satisfying tan x = cos x. Your answers should be expressed in radians, rounded to 4 decimal places. Show all your working. [You will need to use a scientific calculator that has buttons such as sin−1 or arcsin so as to be able to find the angles...
20. ### How to analyze AC using radians and degrees

I just found out V = Acos(wt+phi) is made up of both radians and degrees, where w is rad/s and phi is degree. You have to convert either one to the other to calculate it. Assume phi is 0 degrees. I(t) = Icos(wt), and w is radian/s. So then capacitor impedance is -j/wC. V(t) = (I<0) *...
21. ### AC Signals - Radians and Degrees? Why do we use both?

Why exactly do electrical engineers represent sinusoidal signals with the frequency in terms of radians/sec but phase shift in terms of degrees? Why don't we represent the phase shift in radians? I'm curious where/why this convention originated.
22. ### Wave Number (k) 2pi/lambda = Radians /Unit Distance ?

The wave number k = 2π/λ . But is defined as radians per unit distance. What is the correlation here between the wavelength and radians ?
23. ### Interpreting eiπ in Equation: Radians or Number?

Consider the following equation: eiπ = -1 Is π in that equation just a number or do I need to interpret it as radians ? I mean, if I defined a 'diameterian' so that π diameterians would make the full circle, would the above equation still be correct ? Thanks
24. ### Radians and the unit of rotational energy

Hello everyone I have a question regarding radians and the unit of rotational energy (which has been probably asked several times elsewhere but is still confusing for me :-) ). As I understand radian (rad) is a UNIT that is dimensionless (thus cannot be omitted), correct ? Now if I want to...

Homework Statement Homework EquationsThe Attempt at a Solution So, I got the answer to be 126 radians BUT my answer was wrong because it was suppose to be NEGATIVE 126 radians. Can someone explain why my answer was suppose to be negative?
26. ### Sum and difference with radians.

I think I understand the basic ideas of the sum and difference formulas, I just don't get how to break down say, pi/7 into a form that could be worked with. I could convert it to a degree then back again once I have my answer, but that seems like a lot more work than is necessary. If it were 100...
27. ### Converting Chord Length to Radians: A Confusing Concept?

Homework Statement Coverting Cord length to radians and the other problem is: A ball Radius = 12 CM, rolls 15 M, across the gym floor. Through what angle does the ball rotate? We just started this today and I am very confused by it. the other question is converting 11.6 CM Chord Length into...
28. ### How to convert m/s to radians?

Homework Statement the question is a particle move in a circle of radius 20cm with a linear speed of 10 m\s find angular angular velocity ! i have tried it many time's but it didn't workedHomework EquationsThe Attempt at a Solution [Moderator note: Question content moved here from second post]
29. ### What is the notation for angular distance travelled?

What is the notation for the angular distance traveled by an object moving in circular motion? s is for regular distance (m,ft,inches, etc.). What I want is some x to be the distance in either degrees or radians. How should I call that x?
30. ### MHB Find K in Radians: Integer Solution

Find $K$, an integer and is in radians, such that $\sin K>\sin \left(\dfrac{11\pi}{60}\right)$.
31. ### MHB Converting between arcseconds and radians

Hi i need to convert 0.05 arcseconds into radians and am not sure where to start any help is appreciated. thanks
32. ### MHB Find x (Radians): Solve sec(2π/3 + x) = 2

If sec(2pi/3 + x) = 2, what does x equal? So far I changed it to cos by dividing 1/2. And then, I changed the 1/2 to radians which is pi/3. But, I'm not sure what to do next.
33. ### Radians to measure ac currents

Could someone please explain why is chosen to measure ac sin/cos signals with radians instead of seconds? If ac waves is the behavior of a wave over time? Any feedback would be appreciated. Thank you!
34. ### Derivative as a rate of change exercise

Homework Statement A police car is parked 50 feet away from a wall. The police car siren spins at 30 revolutions per minute. What is the velocity the light moves through the wall when the beam forms angles of: a) α= 30°, b) α=60°, and c) α=70°? This is the diagram...
35. ### Why Should You Learn to Think in Radians for Trigonometry?

I'm a high school senior taking Pre-Calculus. We just recently finished the unit on sequences and series and we are going to be diving into trigonometry. For my homework assignment there are several questions regarding radians. In Algebra 2 Trig, we only briefly learned what radians were, and I...
36. ### MHB What is the rate of change of s with respect to time when y=π/2 radians?

https://www.physicsforums.com/attachments/2883 It was found earlier that $\frac{dx}{dt}=\frac{\pi}{30} \frac{rad}{sec}$ and $\frac{dy}{dx}=\frac{\pi}{60} \frac{rad}{sec}$ (C) since $s$ and $x$ and are related by the Law of Cosines; What is the rate of change of with respect to time...
37. ### (P.15) Angular Measure expressed in radians

Which equation is valid only when the angular measure is expressed in radians? a) α = Δθ / Δt b) ω= Δω / Δt c) ω^2 = ωo^2 + 2αθ d) ω = Vt/r (here T is a subscript) e) θ = 1/2αt^2 + ωαt Answer is D but why?? * I am totally lost so I can not show work
38. ### MHB What is the rate of change, in radians p/s

Point P moves at $a$ constant rate along the semicircle centered at O from M to N. The radius of the semicircle is $10cm$, and it takes $30s$ for $P$ to move from $M$ to $N$. $∠POM$ has measure $x$ radians, $∠OPM$ has measure $y$ radians, and $MP=S$ cm as indicated in the figure. $a.$ What is...
39. ### Radians vs Degrees: Explaining to Cooper

Homework Statement The voltage across a 60μF capacitor is described by the equation vC =(18 V) cos(200t), where t is in seconds. What is the voltage across the capacitor at t =0.010 s? Homework Equations N/A The Attempt at a Solution When you use degrees the answer is 18V and...
40. ### MHB Why e is "natural", and why we use radians.

Many books give bad answers or no answers at all to why we work with base $e$ and measure angles according to radians in calculus. Here is what I tell my students, as far as I know, this is the best explanation I seen because it is essentially a one line explanation that is short and to the...

Just watched a video of another way of thinking of angles , Rational curvature and winding numbers What do you think ?
42. ### MHB Angle $\theta$ Changing Rate of Ladder $13ft$ Long

A Ladder $13ft$ long is leaning against the side of a building. If the foot of the ladder is pulled away from the building at a constant rate of $\displaystyle \frac{2 in}{sec}$ how fast is the angle formed by the ladder and the ground changing in $\displaystyle\frac {rad}{sec}$ at the instant...
43. ### MHB Find angle in radians of tractor wheel going 22 mph in 12 s

the calculation is mine however, if ans is correct not sure what the conventional way would to set this up?
44. ### Rotational motion problems involving radians

Homework Statement The professor gives us an exam preview where he hints at the types of problems via the picture. Attached is the preview. I have a question about pictures 1 and 2. It's probably a problem that involves rotational and translational energy, conservation of energy. If it's...
45. ### Why derivative of sin x is cos x, only if x is in radians?

What differente does it make? As far as I can see it, the limit definition of a derivative shouldn't be affected by the fact that x is expressed in radians or degrees...
46. ### How to Convert Rotations per/sec to radians per second

Homework Statement How do you convert Rotations per/sec to radians/sec Ex: a disk rotates 15 times in 25 seconds convert to radians/sec Attempt: 15 rotations / 25 seconds = 1 rotation / 0.6 seconds 1 rotations = 2 pi rad
47. ### Using radians to discover the lengths of geometric shapes (circles)

Homework Statement refer to question image Homework Equations refer to question image againThe Attempt at a Solution refer to working out image This is my brothers maths homework. He normally doesn't use online methods to request help and this is his first time.
48. ### Convert Radians to Seconds - Solve f(t)=Rsin(ωt + θ)

Homework Statement Given an equation such as f(t)=Rsin(ωt + θ) find the value of f(t) when t=5s Homework Equations N/A The Attempt at a Solution What I'm not understanding is that generally a function sin(ωt + θ) describes what happens when the angle t changes. However the...
49. ### Convert 0.001 arcseconds to radians.

Homework Statement Convert 0.001 arcseconds to radians. I believe the correct solution is 4.85 x 10^-9 radians. Homework Equations 2∏rad = 360° = 60' = 3600'' The Attempt at a Solution The way I was trying to achieve this solution is by setting my calculator to radian mode, typing in...
50. ### Converting periodic function from radians to time?

Homework Statement Hey guys. So I have this homework exercise where I have to convert the following periodic function in radians into a periodic function in time. f(θ) = (80/∏2) θ, -∏/2 ≤ θ ≤ ∏/2 (80/∏) - (80/∏2) θ, ∏/2 ≤ θ ≤ 3∏/2 Homework Equations θ = ω0 t ω0 = 2∏/T...