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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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Why must the coordinates of a point on a circle be sinusoidal as a function of the angle? [on hold]

A defining feature of radians as a unit of measurement is that if an angle $\theta$ is expressed in radians, the height of a point on the unit circle at this angle is $\sin(\theta)$. Is it possible ...
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1answer
24 views

Right Circular Cylinder: Distance between axis and plan

B is a point in the top circle of a right circular cylinder. C is a point in the bottom circle of the given cylinder. The angle between [BC] and the base's plan of the cylinder is 45 degrees. The ...
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0answers
16 views

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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0answers
18 views

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 ...
2
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1answer
37 views

How to find the angle of reflection given 2 points and a mirror?

I'm pretty new to the Mathematics section of StackExchange and need some guidance on some math for a 2d topdown game I am making. In my game there is an Archer boss, who can shoot reflective arrows, ...
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0answers
20 views

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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2answers
29 views

Intermediate Value Theorem in geometry - in angles?

I came across a maths problem, which I reduced to need the following result: If $A,B$ are fixed points, $C,D$ are points not on line AB, and CD is a curve (in this case, a section of the ...
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2answers
35 views

Angle between two surfaces

I have the next question: Find the angle between two surfaces: $x^2+y^2+z^2=9$ and $z=x^2+y^2-3$ at the point $(2,-1,2)$. I have the next formula: $$\cos\theta =\frac{\nabla \Phi _{1}\cdot\nabla \...
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0answers
19 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. ...
2
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1answer
40 views

Is it given that two lines are parallel if a right angle is shown?

If I have a diagram, like the following: And I want to make make a proof for something like how segment AB is $\cong$ to segment AC if segment BD $\cong$ segment DC (using Perpendicular Bisector ...
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2answers
25 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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0answers
27 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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0answers
13 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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1answer
33 views

If a right circular cone has three mutually perpendicular generators then find its semi-vertical angle.

If a right circular cone has three mutually perpendicular generators then find its semi-vertical angle. We see that if $ax^2+by^2+cz^2+2fyx+2gzx+2hxy=0$ has three mutually perpendicular generators, ...
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0answers
10 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 ...
2
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1answer
38 views

Rotation Matrix and Triple Angle Formulas?

Define $R_{\theta}:\mathbb{R}^2 \rightarrow \mathbb{R}^2$ as the rotation matrix by angle $\theta$, where $$R_{\theta} = \begin{pmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \...
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2answers
44 views

Triangle inequality for angles in Euclidean space [duplicate]

Is there any simple proof of the following statement: for all vectors $ v,w,u\in V\setminus\{0\} $, where $ V $ is a Euclidean space, inequality $$ \angle(u,v)\le\angle(u,w)+\angle(w,v)$$ holds. ...
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1answer
40 views

How can I solve x in this shape?

I've been learning angles on lines and in shapes but I've been struggling with how to go about solving this. Usually you're given more angle values or at least a side value as a starting point - ...
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0answers
13 views

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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1answer
23 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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0answers
28 views

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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1answer
36 views

Need help on a trigonometry problem

The question is- Points D and E divide equal sides AC and AB of an equilateral triangle ABC according to the ratio of 𝑨𝑫: 𝑫𝑪 = 𝑩𝑬: 𝑬𝑨 = 𝟏: 𝟐. Edges BD and CE meet at point O. Find ∠𝐀𝐎𝐂. ...
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0answers
18 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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1answer
17 views

Angle required to rotate a polygon towards the direction of a vector

I have a problem where I need to rotate a polygon so it has the same direction as the vector $v_1$ (the pointy head face $y$-axis +ve). I tried a solution where I take two vectors one the $y$-axis: ...
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1answer
28 views

Angle created by three distincts random vertices

Assume you have a regular polygon ( $n$-sides). and Let $A=\{ x_0, x_2, \cdots , x_{n-1} \}$ be vertices of the polygon. My Question is: Are there is any formula that tell us what is the angle ...
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2answers
42 views

To find the bisector containing the point

Given two Non Perpendicular lines $3x-4y+1=0$ and $12x+5y-3=0$ Find the equation of bisector containing the point $(1,2)$ My try: Using the formula for angle bisectors we have: $$\frac{3x-4y+1}{5}=...
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0answers
15 views

Phase angle of a Fourier series

I have read in my textbook that if a Fourier series consists of only sine terms(that is, the function is odd), its phase angle is 0. If the Fourier series consists of only cosine terms(that is, the ...
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1answer
28 views

How do i calculate the angle $\theta_L$?

I need to find the angle $\theta_L$ in the attached sketch. The variables I know are: $R_L$, $R_G$, and $\theta_G$. So i need a formula for $\theta_L$ in terms of these. $R_g$ is also the distance ...
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1answer
36 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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3answers
62 views

Prove that AM is perpendicular to Bh [duplicate]

In the isosceles triangle $ABC$, $M$ is the median of $HD$ and $AH$ is perpendicular to $BC$ and $HD$ is perpendicular to $AC$. Prove that $BD$ is perpendicular to $AM$.
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1answer
79 views

3D rotation defining the intersection of 2 planes

Triangles $DAE$, $DCE$ and $DBE$ form a quadrangle $ABCD$, where $\angle BAD$ and $\angle BCD$ are right angles. I have a scenario in which I want to find the angles $\angle ABD$ and $\angle DBE$, ...
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1answer
21 views

Length across cuboid at an angle

I would like to calculate the change in length across a cuboid when looking at it from different angles (e.g. 10 and 20°). In the illustration below the red arrows show the length I would like to ...
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1answer
26 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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2answers
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For which $\alpha$ will take the cake ever be again with chocolate on the bottom and cream on the top

Question: A bored kid left alone at home decides to take a chocolate cream cake (chocolate on the bottom, cream on top) and his protractor and spend the day as follows: He cuts a slice of angle $\...
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2answers
30 views

Why is the angle between vectors restricted?

Why is the calculated angle between two vectors always between $\pi$ and $0$. Is this due to the limitations of $\arccos\theta$ or is it because angles between vectors is described to be the smaller ...
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1answer
57 views

Geometry triangle inside circle [closed]

Triangle $\triangle ABC$ is inscribed in a circle. $D$ is a point on $AC$. $BD$ is angle bisector of $\angle B$. $O$ is the center of the circle then find $\angle ADO$ if $\angle A=20°$ and $AB=AC.$
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0answers
23 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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2answers
29 views

How many equally spaced points are needed around a circle of radius r such that every point is d units apart from eachother?

This question is a bit different than what I have seen here. I know how to calculate the positions such that n points will be equally spaced around a circle however ...
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0answers
34 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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2answers
54 views

How can I find the sum of the angle $AMB$, angle $ANB$ and the angle $ACB$? [closed]

How can I find the sum of the $\angle AMB, \angle ANB$ and the $\angle ACB$? In triangle $ABC$, $\angle ABC =90^\circ$. $BC$ is divided in $3$ parts such that $BM=BN=NC$. And also $AB=BM$. Here are 2 ...
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1answer
29 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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3answers
32 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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0answers
22 views

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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1answer
67 views

What is it called when you subtract multiples of 360 degrees?

When you divide a vector by its magnitude to get a unit vector, there's a verb for that: you are "normalizing" the vector. Similarly, is there a verb for when you subtract multiples of $360$ ...
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2answers
41 views

Calculate arc central angle given the center, radius, start and end points of the arc

How can I calculate the angle at the center of an arc knowing radius and center, start, and end points? I know how to do that if I have the length of the arc, but in my case I don't have it.
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1answer
45 views

I want to find $\angle BAD$. [closed]

$ \angle BDC = 120°$, $\angle BEC = 160°$. I want to find $\angle BAD$.
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1answer
36 views

Conversion between angle with axis & angle with axial plane

Let's imagine in 3D space I have three angle, $\theta_x$,$\theta_y$,$\theta_z$ respectively with X-axis, Y-axis, Z-axis. Just like $\alpha,\beta,\gamma$ here: I also have $\theta_{xy},\theta_{yz},\...
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0answers
22 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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0answers
19 views

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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0answers
72 views

Is it possible to prove the derivative of sine geometrically without arc length?

There are a great many ways to prove that the derivative of sine is cosine, some of them based on things like the Taylor series definition. I’d like to prove it using only the right-triangle ...