Questions tagged [angle]

An object formed by two rays joining at a common point, or a measure of rotation. In the latter form, it is commonly in degrees or radians. Please do not use this tag just because an angle is involved in the question/attempt; use it for questions where the main concern is about angles. This tag can also be used alongside (geometry).

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How would I rotate an Euler angle?

Given an orientation given as an Euler angle, how would I rotate this Euler angle? I assume simply multiplying the angle with a rotation matrix is not a valid approach. For example I am measuring an ...
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Complete characterization of equiangular polygons with two alternating edge lengths

I am looking for a complete characterization of equiangular polygons with two alternating edge lengths. Also self-intersections are allowed (as seen here https://en.wikipedia.org/wiki/Isogonal_figure ;...
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Change double integral into two convolutions

I'm looking to change a double integral into convolution from the original integral, which is $$S(z_0,\Omega) = \int_{4\pi}\frac{H\!\left(z_0,\Omega,\Omega'\right)}{4\pi}\int_{z_0}^{\infty}F\!\left(z'...
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Bound on norm of difference of two vectors using their angle

For two unit vectors $u$ and $v$, prove that if $$\sin(\angle u,v)\leq l$$ We have: $$\exists \theta\in \lbrace -1,1\rbrace :\quad \|u-\theta v\|_2\leq\sqrt{2} l$$ I see this in the application of ...
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Length of line projected onto a horizontal line at some angle.

Please see the image to understand my question: Given the angle theta, and 3 parallel lines, the top line being 5 unit distances away from the middle line. How do ...
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46 views

Absolute Value of Vector with only 2 values and one Angle?

How do I calculate the absolute Value of a Vector when I only know the Values of two Vectors and the angle between them? The Vector I wanna find is the resulting Vector after you add the other 2. ...
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33 views

finding third point, provided two points , an angle and the length from one of two given points

I have gone through many of the answers and I have not a suitable one so I am asking this question As provide in the reference image I have been provide two points A(x, y) and B(x,Y), an angle Θ ...
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30 views

Trigonometry Angle Addition and Subtraction

I'm working on a problem. The problem is boxed in Blue. Ignore the right side boxed in green, it's unreleated. Inside the blue box, I have highlighted in green where my error is when solving this ...
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330 views

Scale cosine similarity between vectors to range 0, 1?

I am interested in calculating similarity between vectors, however this similarity has to be a number between 0 and 1. There are many questions concerning tf-idf and cosine similarity, all indicating ...
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41 views

rotate plane according to pitch,yaw and roll

Lets say, i have ground-plane equation = $ax + by + cz + d$ . Then, i rotate camera and i know new yaw ( $\theta$ ), pitch ( $\alpha$) and roll( $\gamma$) angle of camera. How can i calculate new ...
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Proving plane geometry problem

Given 8 lines on a plane and no two of them are parallel. Prove that, at least two of them form an angle less than 23°. I have checked this out using different angles and the statement seems to be ...
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50 views

Phasor/Harmonic Addition Formula/Theorem: Why can we take out the frequency out of an complex argument?

Harmonic Addition Theorem Harmonic Addition Formula Phasor Addition Theorem Phasor Addition Formula Those four name can be used as a keyword on google. I haven't known the official name and think ...
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Need help on a problem on trigonometry

In triangle ABC, AB=10, CA=12. The bisector of ∠𝐁 intersects CA at E, and the bisector of ∠𝐂 intersects AB at D. AM and AN are the perpendiculars to CD and BE respectively. If MN=4, then find BC. ...
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37 views

Move a point in 3D space a given distance and angle

so I'm fairly new to maths and need to know how to move a given 3D point in space, a certian distance and a certian angle and get the new position, that angle being in radians and being an x angle and ...
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40 views

What is the length of the arc on the unit circle subtended by an angle of 120 degrees? Show all work.

What is the length of the arc on the unit circle subtended by an angle of 120 degrees? Show all work. 2/3 1/3(pi) 2/3(pi) pi I used an equation where the central angle equals the arc length divided ...
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1answer
47 views

Making a formula that finds the horizontal and vertical distance between two points that change with a new angle.

I am making a Scratch 3.0 game. The shooter sprite is holding a gun slightly off-centre (see images), and I need the bullet to go to the end of the barrel of the gun before travelling forward (as so ...
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26 views

Signed angle between higher-dimensional oriented vectors?

I am working with vectors in $\mathbb{R}^4$. Any two such (non-parallel) vectors obviously define a plane, and I can rotate any vector in the plane defined by itself and a second vector as follows: $...
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37 views

Calculating the missing angle

I have the following problem where I need to find out the missing the angle. I have to apply some triangulation method to solve. I have the values of the hypotenuse. My solution is to break this ...
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1answer
85 views

Apply pitch/roll measurements to different reference frame

My problem is identical to this unanswered question. IMU orientation reference image I have an IMU mounted on an object at an angle offset with that object's pitch and roll axes. When I get pitch ...
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54 views

angle and coordinator calculate from two points forming a line

Two points are given: $A (x_1, y_1)$ and $B (x_2, y_2)$. These points form a line. At point $B$ is the end of the line. I need to calculate the angle that is shown in the figure and also the ...
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If angles can be vertical, can they be horizontal or slanted?

IMPORTANT: The angles are named vertex-point on leg-point on leg. Angles are vertical if they share a vertex. $\angle ABC$, $\angle ACD$, $\angle ADE$ and $\angle AEC$ are vertical. Angles are ...
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31 views

pass Euler angles from a coordinates system to another

I have a coordinates system $(\vec{x},\vec{y},\vec{z})$. In wich there is three known perpendicular vectors of length 1 that define another coordinate system: $(\vec{x'},\vec{y'},\vec{z'})$. ...
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Distance between two points at same angle in trochoid curve

Anyone please help me to find out the distance in following case. Refer to the attached image. Consider an arbitrary point P on the circumference of a circle of radius r (mm). The point makes an ...
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44 views

Is there a conformal mapping from the surface of a cube to the surface of a spherical cube that preserves edges?

Is there a conformal mapping (with certain singularities noted below) from the surface of a cube to the surface of a spherical cube that preserves edges? Note that this also implies that vertices and ...
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24 views

angularly and lineraly accelerating particle

Let's say there's this particle that moves with a unit of time. Let's say this particle has a linear velocity and acceleration ($v$ and $a$) and an angular velocity and acceleration ($v_\theta$ and $...
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Calculate the area of a parametric sector

I encountered the following definition: $\forall tD_t=\{(x,y)\in R^2:\theta(x,y) \in [-\pi,t]\}$ where $\theta(x,y)$ is the angle in $[-\pi,\pi)$ that the vector $(x,y)$ forms with the x-axis. ...
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20 views

How can I check which face of spherical polyhedron corresponds to a given euler angle?

I am specifically mapping a dodecahedron to a sphere and I am trying to get if a rotator is within the boundaries of a given face. Thank you
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117 views

extracting Angles from a Rotation Matrix

How to extract the angle a from the rotation matrix, given by: ...
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Requirements of 3 proper Euler angles

Why do proper Euler Angles all come in the form of xyx, yzy, xzx, xyx, and etc? Also, why is the third one needed if it rotates around the same axis as the first one? How I'm seeing it right now, each ...
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25 views

Calculate angle

What angle is between vector a and vector b if the angle between vector p and vector q is 90°, where vector p=5a-2b and vector q=-3a-6b? (Yes this is homework)
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28 views

Is it possible to calculate the sides of a triangle with the angles and the length from tip to base?

Is there an equation to calculate the length of a triangles sides given only the angles and the length from the tip of the triangle to its base? If so please express the equation using the following ...
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71 views

Another variant / corollary of Langleys adventitious angles triangle problem

I recently came across an elegant simple method on Youtube to solve the original Langley's problem using basic geometry principles. Worlds Hardest Easy Geometry problem I have also gone through ...
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55 views

Quaternion angle calculation

I'm working on a programming project, in this project I'm receiving an angle as a quaternion value, I partially understand how they work but I don't find any math to get the values I need. What I ...
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2answers
23 views

Rotation of $e_1 \in \mathbb{R}^n$ in angles along the axis

I have the vector $e_1=(1,0,...,0)^T$ in $\mathbb{R}^n$. I would like to rotate it by angle $\theta_2$ along axis $x_2$, resulting in the vector $r_1 = (\cos(\theta_2),\sin(\theta_2),0,...,0)^T$. ...
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38 views

Curvilinear abscissa = radius * angle - Circular motion

I would like to understand why: $$ s(t) = r \, \theta(t) $$ where $s$ is the curvilinear abscissa, $r$ the radius and $\theta$ the angle in circular motion. Thank you for your time.
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How to know when a 360 rotation was performed around any given axis?

If I have any given axis, e.g. $\frac{1}{\sqrt{2}}\left[ \begin{array}{ccc} 0 & -1 & 1 \end{array} \right]$ and a rotational speed of $\omega = 1.5$ [deg/s] around that axis. How can I check ...
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1answer
36 views

Angles of convex polygons

For a convex polygon, show that the sum of any two interior angles is greater than the difference between any two interior angles. (the polygon has more than 3 sides) If I pick 4 dots A,B,C,D and say ...
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45 views

calculate angle of line with negative slope

I want to use the formula $$ tan(\alpha)=m $$ for negative slopes but always get negative degrees. For instance, say the slope of a line $g$ is $-1$. Using the formula above (arctan$(-1)=\alpha$), I ...
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76 views

Simply find point in circle border

This seems to silly for you expert guys in math but I am not good in this So Please help. Suppose you have clock of 330 * 330 pixels so I have radius 165 in circle. I want to find position of ...
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When the slope of the angle bisector is 1, is the product of the slopes of the 2 lines forming the angle equal to 1

When the slope of the angle bisector is 1, I have been told that the product of the slopes of the 2 lines forming the original angle is 1. Is this true?
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Finding the location of points of a triangle given the angle and length ratio.

Given that a point P is located at (-2.5,4.33) I need to locate the points A and B such that $\frac{PA}{PB} = \frac{4.77}{8}$ and $\angle APB = 55^o $. A and B must be on the -ve part of the x axis. ...
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116 views

Orthogonal unit vector in spherical coordinates

A particle is traveling in the direction of the positive $z$ axis, until eventually, it is deflected. The new direction is given by an azimuthal angle (w.r.t. the positive $z$ axis) $\theta$ and a ...
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Prepend a vector with 90 degree angle to an existing one

First of all: my knowledge in mathematics is a bit rusty, so no matter how simple my question is, I afraid I in every case need a somewhat detailed answer: I have a line from coordinates (x1,y1) to (...
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34 views

Should dot product must be applied on values of same scale

I have points in $n$-dimensions. I want to find the points which lie on one side of the plane and other lies on the second side and i'm trying to do this with the help of dot-product. Suppose i ...
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199 views

Cardan (or Tait-Bryan) angles z-x-y and rotation matrix - Proof

I'm trying to get the following rotation matrix (cardan angle sequence z-x-y): To do that, I multiplied the three elementary rotation matrices $R_zR_xR_y$, but the result is different: Can you tell ...
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59 views

What is the angle from (0,0) to (longitude, latitude)?

Starting on the crossing between the equator and the Greenwich meridian (0,0), one can proceed to any point on Earth with a given longitude and latitude along a great circle. Seen from the centre of ...
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74 views

Calculate new point of line when changing the angle

I got 3 Points which form an angle alpha. How do i calculate the new location of Point3 when the alpha is changed? Point1 and Point2 stay staionary.
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Geometry of angular variables

Angular variables have an interesting property in that for some applications, e.g. angle at which the light beam of a lighthouse is pointing, we expect some functions of that variable to not depend on ...
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22 views

Compute the angle of the tangent line to space defined by a curve

I"m taking multivariable calculus and I'm being given the curve $\vec{r}(t)= e^t \textbf{i} + (cos^2t + 1) \textbf{j} + (-t^2 + t - 1) \textbf{k}$, the point $P_0 = \vec{r}(0)$ and the yz-plane. I ...
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304 views

How to determine Euler angles of ZYZ rotations?

Consider a point $\mathbf{P}=(x \ y \ z)^\text{T}$ which is transformed into $\mathbf{P'}=(x' \ y' \ z')^\text{T}$ in counterclockwise direction according to the ZYZ convention as follows: $\begin{...