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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Deriving Formula for internal and external angles of a concave polygon

How to derive formula for internal and external angles of a concave polygon. The internet shows that the formula is same as a convex polygon, but how can we derive it? Thank You.
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Is there a term for angles which are coterminal with 0?

Quite simply, is there such a term, either an adjective, as in such an angle is called a [insert word here] angle or a noun as in such an angle is called a [insert word here]? Because I feel like it's ...
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401 views

Angle from rotation matrix

I have an exam later today and I have come across something which is not covered in my lecture notes (that I know of) that I need to know the answer for! Could someone please explain to me how you ...
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109 views

Sums of angles and trigonometric values

Are there any formulae where an angle and e.g. the sin of an angle are added/subtracted together. I know of infinite series such as, $\sin\theta=\frac{\theta}{1}-\frac{\theta^3}{3!}+\frac{\theta^...
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1answer
244 views

Rotating Around A Regular Polygon in Polar Coordinates

I don't know if I have my phrasing correct here. I am basically trying to get the radius around the parameter of a regular polygon. From here on I will just use a pentagon for a concrete example. ...
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2answers
52 views

How to find out the angle here

Let $ P $ be an interior point of $ ∆ABC $ , such that $ Q $ and $ R $ are the reflections of $ P $ in $ AB $ and $ AC $ respectively. Also it is given that $ Q,A,R $ are collinear. Then i need to ...
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1answer
34 views

Finding a vector within a specified range of angles from other vectors

Take $v_1,v_2,\ldots,v_k\in \mathbb{R}^n$. Is there a way of finding some $x\in\mathbb{R}^n$, given the inequalities $l_i\leq\theta_i\leq u_i$ where $\theta_i$ is the angle between $x$ and $v_i$, or ...
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167 views

Angle between a spline point and the tangent to the previous point on spline

I have spline points represented as geographical points (latitude,longitude) and I want to compute the angle between the current spline point and the tangent to the previous spline point.
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2answers
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should I insert angle in radians or degrees for sun radiance model (sinusoidal)?

If I have the following model function for sun radiance through a day, $$ P(h) = 0.3 \pi \sin(\frac{h\cdot\pi}{12}-\frac{7\pi}{12}) [\frac{kWh}{m^2}] $$ Where $h$ is the hour of the day and the ...
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44 views

Finding an angle using image data

I am trying to recreate classic light guns on LCD TVs by using object detection from an image. I have a light gun that will have a colored dot on the end of it. The webcams at either side of the TV ...
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44 views

Sum of angles between three intersecting spheres

I've been writing a survey on Thurston's construction of a hyperbolic structure on the complement of the figure-eight knot. At one point it is important that the sum of the angles between three ...
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18 views

How to produce rotations with no repetitions of a volume using Euler angles?

I have a volume (which can be written as an array) and need to make an algorithm to produce a set of rotations of this structure using different combinations of Euler Angles with a fixed step. For ...
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304 views

How do I calculate a real angle between two Euler angles?

I have a set of 2 Euler angles. I want to first rotate the vector $(0,1,0)$ with each Euler angle and then calculate the angle between 2 normalized vectors. But I don't know how to do this in ...
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1answer
25 views

Formula for bisector segment of a given lenght between two segments

I've got the (x,y) coords of three points defining two connected segments; I need to find the coordinates of the two bisectors, of a chosen lenght, at the angle between the two segments. I have ...
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104 views

Differential Geometry - Holonomy Angle

Let $M$ = $S^2$ = ${\{(x, y, z)\in\mathbb R}$; $x^2+y^2+z^2 = 1\}$ $\gamma = \gamma_1 \cup \gamma_2 \cup \gamma_3$ where $\gamma_j$, $j = 1, 2, 3$ is given below: $\gamma_1 = \{(cost, sint, 0)\ |\ 0\...
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36 views

Sides lengths of a tetrahedron from top angles and base dimensions

For a (possibly irregular) Tetrahedron $ABCD$, if I know the lengths of $AB$, $BC$, and $CA$ and the measure of $\angle ADB$, $\angle ADC$ and $\angle BDC$, is there a way to find the lengths of sides ...
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363 views

Measure of Angle for an isosceles triangle between parallel lines

Two lines are parallel and there is a transverse line passing through both. There is an isosceles triangle as shown in the figure. angle x measurement is given as 8, and the problem is to find out ...
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1answer
390 views

Finding the value of theta using the $6$ trigonometric functions on an $xy$ plane.

Here's a link of what I am trying to learn about. http://www.webpages.uidaho.edu/learn/math/lessons/lesson03/3_05.htm Now I have one question. How will I find the value for theta in each function ...
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27 views

How come the angle for cross and dot equations are not equivalent in these equations?

Finding the angle between two lines Given lines: $$l_1 = [3, 1, -1] + t[2, -2, 3]$$ $$l_2 = [5, -1, 2] + t[1, -3, 5]$$ I tried cross product equation of finding the angle: $\cos^{-1}(\sqrt{426} / (\...
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324 views

The angles of the triangle given the position vectors of the triangle using the scalar product

I can't seem to show for question (a), I am not sure if it's because of my wrong calculation, or is it the question has the wrong values? What I have done is I used the scalar product. I found that ${...
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1answer
643 views

Weighted average of multiple angles

This answer has a good approach to calculating the average between multiple angles: simply convert each angle to its unit vector, add them up and convert the resulting sum vector back to an angle. The ...
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718 views

Proof: Angle between two diagonals of a parallelogram

Can anyone prove the angle $\theta$ (smaller angle) between diagonals of a parallelogram is given by the equation $$\cos(\theta)=\frac{a-c}{a+c}$$ where $2a$ is the base length of parallelogram; $2c$...
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597 views

Having trouble finding an angle given an equation including radians (statics equilibrium problem)

I'm doing some Engineering Mechanics homework regarding equilibrium of rigid bodies and I've come across a problem involving radians that has stomped me. I have the question and the steps to find the ...
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1answer
57 views

how to Get Angle of diagram

What is $\angle{CAD}$ ? What i tried using all angle properties opposite side of angle etc but i guess my angle $\angle{CAD}$ is wrong
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1answer
131 views

Moving a group of rotating objects.

I have some objects that rotate around a common center, the formula I use to calculate their rotation is something like: Math.cos(angle) * radius; Math.sin(angle) * radius; in every frame I update ...
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1answer
601 views

Length of an arc of a circle when the angle is infinitesimally small

The task is to express the length of an arc of a circle trapped between two radii named $r$ if the angle between them is infinitesimally small, named $d\theta$. The solution to this problem is ...
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1answer
21 views

Calculating angle made with center of room - am I doing this correctly ? What method can I use?

The room Note: it is say supposed to say 4,0 for the first location. 4,4 refers to the center of the room. Basically I have cameras placed in those three locations - (4,0), (0,8), and (8,8). I want ...
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23 views

How an N dimensional rotation matrix can be constructed with more than one degree of freedom

Say we have a point or a line in a three dimensional space, which we can rotate it around the origin by two angles, one with respect to axis 1 and the other with axis 2 or 3 (two angles(degrees of ...
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1answer
33 views

i cant find $\tan\theta$ i think i need to use ratios or similarity some how

if you can help me with finding $\tan(\theta)$ it would help me a lot, as I wanna know how to do it and what identities to use, possibly triangle similarities or something to do with ratios question #...
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24 views

How to find the angles of a trapezoid

The perimeter of a trapezoid is 5 and the lengths of its sides are integers. What are the smallest two angles of the trapezoid. The perimeter is 5 so I get 1*2+1*1+2*1 as the sides. But how do I ...
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41 views

Simple Geometry: Best angle to view trees from fixed camera

I am trying to solve this question: Given a fixed camera in a forest (with predefined trees), give the best angle in which the camera pictures the maximum of trees. The solution I have come up ...
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53 views

Proving a formula in geometry

I've the following diagram given: The two main lines are parallel. Theorem: $$\left|\text{GG}'\right|=\left|\text{KM}\right|\sin\varphi-\left|\text{KG}\right|\sin\varphi=\left|\text{GM}\right|...
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Mirroring an angle over the Y axis

This question is a follow-on from this one posted on Stack Overflow. I'm working with an application that uses a function to calculate the points on an arc given the following information: Start ...
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23 views

Angle between two vectors: 3D No magnitudes and/or sqrt()

Hey so I have a very efficient method to calculate the the components (x,y,z) of two vectors, and I want to calculate the angle between them. I am computing this for about 8 million individual entries....
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Finding an interior angle between two interior angles

In the picture below; shows how it is illustrated: https://imgur.com/a/2DVsM4x I am trying to find angle b; given angles a and c. The value for angle a is 32 degrees, and for c it is 77degrees. How ...
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How to add 42 degrees to either the X/Y/Z axis in quaternions

The picture below is showing a human bone. Red is the bone/object (humerus bone/the bone on your bicep) Orange is X axis Purple is Y axis Pink is Z axis Link to image If the current rotation of the ...
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Angles between normal vectors vs angles between faces

I am to prove two different formulas, but I don't get how are the values in the formulas different. This is a tetrahedron problem, specifically angles. At first, I am supposed to prove $\ A^2 = B^...
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Can the projection of two vectors be used to approximate the angle between them?

I am supposed to use a secondary justification (other than using the inverse cosine of the dot product divided by magnitude) that the angle between two vectors (117.429 degrees) is obtuse. The two ...
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2answers
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Finding side length from two scalene triangles with common angle and side and ratio between sides. Trigonometry

I have two scalene triangles with a common angle and side. I would like to find the length of $x_2$. I have all variables in green: the angles $\angle$ B,$\angle$ C,$\angle$ D,$\angle$ E and side "...
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Math formula for Real life distance to phone screen adjustment

Please help me! The picture below will give some depiction of what i'm creating. I'm trying to create a smartphone application for straight road construction control. The idea is to let this app ...
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1answer
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Angles and rates of change

I'm trying to get my head around the following problem, any help is appreciated. My maths skills aren't the best, so apologies in advanced for its stupidity. Say I'm in a car, and I'm driving ...
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29 views

Wrapping around a vertical facing angle

$a$ is a vertical facing angle in 3D space, it can be from -90 to 90. I need to add $b$ to it and have it result in a vertical angle "wrapped" around to the other side with the horizontal angle facing ...
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49 views

Transformation that do not modify angles

How can I prove for $R_2$ that the matrix $$T = \begin{bmatrix} a & b \\c & d \end{bmatrix} =\begin{bmatrix} a & b \\-b & a \end{bmatrix} $$ is the ony one that, when multiplied with 2 ...
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Geometry that models complex angles

In Euclidean geometry, the angle between two lines is real. In hyperbolic geometry, the angle between two crossing lines is real, and one between two parallel lines is imaginary. What about general ...
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Parametrizing a projection with angles

I want to estimate the parameters of a linear regression, with y as a function of orthogonal standardized vectors x1, x2 and x3. however, for various reasons, I want to keep constant the variance and ...
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28 views

convert euler angles to individual rotations about x, y and z-axis

I'm doing some orbital mechanics and have calculated the Keplerian Elements (Euler angles) and now I want to plot it in 3D but I'm constrained to only doing rotations about the x, y or z-axis. I've ...
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Is there a unique correspondence between X,Y,Z axes of a coordinate frame to the yaw, pitch, roll axis

As shown in the figure below, yaw, pitch, roll corresponds to rotation about Z,Y,X respectively. Is this correspondence unique? Can we can have yaw, pitch, roll to correspond to any permutation of X,Y,...
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37 views

Find angle between two vectors relative to a normal

I'm making a simulation which requires random movement and sometimes requires homing to some points. I do the movement through random angles and need the same principle for homing towards a point. ...
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Calculating the angle tilt using an accelerometer

I'm trying to determine the height of a little tree using only an application (PhysicsToolbox on Android) that serves as an accelerometer on my phone. After launching the measurement, I aimed with my ...
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52 views

How to convert Euler's angles and a radius to spherical coordinates?

I'm working on simple blender (3d modeling software) add-on, and I need to convert Euler's XYZ rotation and a radius value to spherical coordinates (The center of a sphere is at (0,0,0)). How to?