{\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.
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...
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!
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...
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...
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...
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
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...
$$0 = 2π/3$$.
$$π/6 =3π/4$$
$$π/4 = 5π/6$$
$$π/3 = π$$
$$π/2 = 3π/2$$
$$2π = 2π$$
$$π/2 + 3π/2 = 4π/2$$
I find this a little confusing but quite wonderful. But, what is it?
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?
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
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).
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?
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?
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...
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...
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) *...
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.
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
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?
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...
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...
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]
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?
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.
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!
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...
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...
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...
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
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...
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...
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...
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...
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...
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...
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
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.
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...
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...
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...