The Angles (Old English: Ængle, Engle; Latin: Angli; German: Angeln) were one of the main Germanic peoples who settled in Great Britain in the post-Roman period. They founded several kingdoms of the Heptarchy in Anglo-Saxon England, and their name is the root of the name England ("land of Ængle"). According to Tacitus, writing before their move to Britain, Angles lived alongside Langobards and Semnones in historical regions of Schleswig and Holstein, which are today part of southern Denmark and northern Germany (Schleswig-Holstein).
Hello,
I am a high school math teacher and recently presented my students with an intriguing problem: "At any given moment, there are two antipodal points on Earth (180 degrees apart) that have the same temperature." This can be demonstrated using one great circle with two opposite points. If...
I'm not sure how to go about solving this mathematically? In just using what seems obvious, I know the angle pi would work, because pi = -1, and 2pi = 1. However, as far as manipulating the equations in a way where it can solve itself without me having to look at a chart where cos for both x...
Question: What is the relationship between the sum of the angles of a non-euclidean triangle being greater or less than 180 degrees and the definite breaking of the parallel postulate? Is the proof of this trivial?
Edit: Additionally, can we say that if the angles of a triangle sum to greater...
Hi, I got a set of Euler angles and a set of quaternions, and I wanted to compare each set against its corresponding set obtained from STK, and I was wondering what would be a good indicator to measure the error between the Euler angles I got and those from stk , and the same for quaternions...
For a better understanding of this exercise here is the image illustrating the scenario described in the statement:
So to solve this exercise I began by drawing a forces diagram:
I believe I have explained everything in the "Relevant equations" section. What am I doing wrong? The book that...
My challenge was on trying to determine the angles: My approach;
came up with a number of equations: ie
##m+n=70^0##
##r=p+40^0##
##q-2r=100^0, ⇒ r=50^0 + \dfrac{1}{2} q##
then it follows that,
##2q+100^0=180^0##
##⇒q=40^0, r=70^0, p=m=30^0, n=40^0##
##m+40^0+t=180^0, ⇒t=110^0##
and...
(This has continued to bother me. I tried asking, and no response. May I please try again?)
Using Euler angles, we rotate about an axis (often, axis three of a gyroscope frame), then a second (axis one of the gimbal frame), then return to the same axis as the first one (back to axis 3, but of...
Problem statement : I copy and paste the problem as it appears in the text. I hope am understanding its wording correctly.Diagram : The river is shown in blue. The two roads start from the crossing C and end in A and B, making angles ##60^{\circ}## and ##30^{\circ}## resectively. The longer of...
Problem Statement : The statement appeared on a website where a different problem was being solved. I got stuck at the (first) statement in the solution that I posted above 👆. Here I copy and paste that statement from the website, which I cannot show :
Attempt : To save time typing, I write...
I want to know if there is any proper relation between the angles of a vector with the three dimensional coordinate axes,
if the angles are ,α , β and γ,
will the sum of α, β and γ be 180 degress
that is α + β + γ = 180°,m finding the same to be true in a 2 D case where α + β = 90° and γ =...
Top-Down-Perspective:
At first I am quite sure that the problem is not solvable since there are that many unknowns.
But my Approach would be to create a linear function with P1 and P2 and then set it equal to the function that gets me the impact location of P3 and then solve it by b3.
Thanks...
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...
Dear Forum,
say I am projecting an ellipsoid along the z-axis to the xy-Plane. The resulting ellipsis is rotated around the z-axis by the angle gamma until the principal axes coincide with the x- and y axis.
Now before projecting, I rotate the ellipsoid first around the z- and then around the...
Good Morning!
I understand that the definitions and notations used for Tait–Bryan angles are similar to those described above for proper Euler angles, and I can work problems in either. However, I lack the ability to "rise above both" and categorize them.
I do understand that the only...
So the Euler's angles are described like this:
xyz-x'y'z' (first rotation around z axis)
x'y'z'-x''y''z'' (second rotation around x')
x''y''z''-XYZ (third rotation around z'')
So I've been thought it goes like this, now I'm wondering why? Why exactly these angles and why this order? Why can't it...
We know the time it takes the water complete the whole parabola is (sin(x) * 6.5 * 2) / 9.8.
So I come up with (sin(x) * 6.5 * 2) / 9.8 * cos(x) * 6.5 = 2.5, because the x component of the velocity is the same for the whole time.
But I get the results like these: x≈0.30929171+πn,1.26150461+πn...
The official solution says ±25.4°, but I'm having trouble reproducing it. Here is my solution:
1) The components of the velocity of firework F with respect to the ground G in the moment of explosion are the following (Notice, I'm using sin, because the statement says 30.0° from vertical.)...
If I have a triangle on a sphere with two of its angles 90 degrees each, do I conclude that it's isosceles and that the shortest distance (on the sphere) beteeen the base and the vertix of the thid angle is 1/4 the circumference of a great circle on the sphere?
This is the picture I have in...
I don't want to post this in a math forum because it's very basic and I just want a straightforward answer, not something math heavy . What's the definition of angle in a cuved space embedded in a higher eucledian space? Like when I have a spherical surface in 3d eucledian space and want to work...
Summary: Each angle has a different type of corner, rectangular, circular, and triangular. Which one is the strongest?
All three angles are mounted in the ground and made of the same material. The same force ‘w’ towards the ground is acting on all angles, which one is the strongest?
Please...
In a triangle ABC, let D and E be the intersections of the bisectors of the angles ABC and ACB with the sides AC and AB, respectively. Knowing that the measures in degrees of the angles BDE and CED are equal to 24 and 18, respectively, calculate the difference in degrees between the measures of...
I have actually already partly solved a), as I do get the concept behind how to find tension through making sure that the net force in the x and y direction are zero.
Here are my answers for a)
T1 = T5 = 2mg/sin(theta)
T2 = T4 = mg/sin(phi)
T3 = mg*cot(phi)
The reason I am asking this...
Suppose I have two intersecting planes in a four dimensional space. It seems to me that there are two angles between these planes. If the two planes intersect in a line then one of those angles is zero. If the two angles are non-zero then the planes intersect in a point. If one plane is the...
NOT a home-work / college question, merely wondering...
Just as there are 'interesting' numbers, per primes, Pythag' triples, Euler-stuff etc, are there any 'interesting' angles between 10~~25º ??
I've had a hunt around, noticed several possibilities invoking eg transcendental fractions of...
I am looking for a formula.
From a horizontal plane of 100 meters; If angle on the left is 8 degrees and the angle on the right is 21 degrees at what distance from the centre of the horizontal plane will these two angles converge?
Summary:: I have a series of three equations that transform three angles of a system (J1, J2, J3), into three spatial x, y, z coordinates. I want to invert them to find the angles from the coordinates.
Reference: https://www.physicsforums.com/forums/general-math.73/post-thread
I have a series...
Problem Statement : I copy and paste the statement of the problem directly from the text.
Attempt : I wasn't able to go far into the solution. Below is a rough attempt.
##\begin{equation*}
\begin{split}
\sin^2A-\sin A\sin B+\sin^2B-\sin B\sin C+\sin^2C-\sin C\sin A & = 0\\
\sin A(\sin A -...
I am trying to follow the work to this question but am stumped at steps 3 and 4.
I am confused as to where the cos^2(90+θ) comes from? I can see it is used to invoke sin into the equation since we have that value. Is it because we are only measuring the x-component of the movement, so we need...
The correct solution uses angles and trigonometry. My solution is as following:
- Suppose the forces exerted by friends 1 and 2 are F1 and F2 respectively.
- There are no net force in the x-direction, so F(total x) = 0.
- F(total y) = F1 + F2 - mg = 0 (initially). Rearranging gives g =...
Problem Statement : Let me copy and paste the problem as it appears in the text :
Attempt : I haven't been able to make any significant attempt at solving this problem, am afraid. I tried to reduce all the higher submultiple angles ##2\theta, 4\theta, 8\theta## into ##\theta##, but the...
I have been doing the resolutions of vectors on x and y-axis with making triangles and reference angles in all quadrants. But I want to calculate now how to find something like ##\sin 235## without the help of reference angles. I know we don’t need to. Calculator and Taylor theorem is handy here...
From @fresh_42's Insight
https://www.physicsforums.com/insights/10-math-things-we-all-learnt-wrong-at-school/
Please discuss!
We all live on a globe, a giant ball. The angles of a triangle on this ball add up to a number greater than ##180°##.
And the amount by which the sum extends...
I thought I understood it until I found the statement mentioned. It's obvious having a look at Figura 3.53:
##\cos \alpha=\dfrac{OP_1}{OP}\Rightarrow{OP_1=\cos \alpha}##,
##\sin \alpha=\dfrac{OP_2}{OP}\Rightarrow{OP_2=OP\cos \left({\dfrac{\pi}{2}-\alpha}\right)=OP\sin \alpha}##
Please Help.. I am struggling to answer this inspite of trying to re read theorems.. I couldn't answer anything.. if you can solve this please teach me the steps.
So i could answer them in the future..
Hey! :giggle:
Make a drawing for each of the values of the angle below indicating the angle at the unit circle (in other words: $\text{exp} (i \phi )$) and its sine, show cosine, tangent and cotangent.
Give these four values explicitly in every case (you are allowed to use elementary...
Part (a)
Ok so for (a) ##\theta_{incident} = \theta_{reflected}##, so I assume I could just consider the horizontal planes in these atoms.
##n\lambda = 2a\sin(\theta)##
##p = \frac {h} {\lambda}##
##\frac {nh} {2amv} = \sin(\theta)##
## v = \frac {nh} {2am\sin(\theta)}##
I suppose the...
We have some potential that depends on slowly varying parameters ##\lambda_a##. Using the angle-action variables ##(I, \theta)##, the claim is that we can define a two-form$$W_{ab} = \left\langle \frac{\partial \theta}{\partial \lambda_a} \frac{\partial I}{\partial \lambda_b} - \frac{\partial...
I am trying to understand the properties of the ##SO(3)## Lie Group but when expressed via Euler angles instead of rotation matrix or quaternions.
I am building an Invariant Extended Kalman Filter (IEKF), which exploits the invariance property of ##SO(3)## dynamics ##\mathbf{\dot{R}} =...
In Chapter 4, derivation 15 of Goldstein reads:
"Show that the components of the angular velocity along the space set of axes are given in terms of the Euler angles by
$$\omega_x = \dot{\theta} \cos \phi + \dot{\psi} \sin \theta \sin \phi,
\omega_y = \dot{\theta} \sin \phi - \dot{\psi} \sin...
Hello,
I didn't understand the geometry of molecules in which central atom has no lone pairs of electrons. for example, in $CH_4, NH_4^+$ molecular shape is tetrahedral and bond angle is $109.5^\circ$. How is that bond angle computed? $CH_4$ stands for liquid methane and $NH_4^+$ is a...