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).

In plane geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane. Angles are also formed by the intersection of two planes in Euclidean and other spaces. These are called dihedral angles. Angles formed by the intersection of two curves in a plane are defined as the angle determined by the tangent rays at the point of intersection. Similar statements hold in space, for example, the spherical angle formed by two great circles on a sphere is the dihedral angle between the planes determined by the great circles.

Angle is also used to designate the measure of an angle or of a rotation. This measure is the ratio of the length of a circular arc to its radius. In the case of a geometric angle, the arc is centered at the vertex and delimited by the sides. In the case of a rotation, the arc is centered at the center of the rotation and delimited by any other point and its image by the rotation.

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Negative angle in radians

I compute an angle of a vector in radians and it is negative (<0, for example _ -5, -150..) I am going to use cordic to compute sin and cos. For cordic I use the full circle ( 0 - 360), positive radian values In degree I can add 360° to convert the…
FrimHart64
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Degrees or radian in Euler's identity?

In Euler's identity, should values in the RHS (the sin and cos part) always be in radians? like $e$ to the power of imaginary $\pi$ is negative one, so if I had $e$ to just the power of $i$, then I would take the radian values of $\cos(1)$ and…
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What exactly is a constant angle?

I previously asked a question about what a non constant angle is but it was closed due to lack of clarity and hence, I'm posting a new question. The notation $x^c$ will be used in this question to represent $x$ radians. So, a proof in my Mathematics…
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A confusion regarding radians

I read in my textbook that radians and real numbers can be considered as one and the same The usual example was given in my book. A unit circle had been taken with $O$ as center and $A$ as any point on its circumference. $B$ was another point on the…
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Find angle and diagonal based on width of a board (carpentry kinda)

Hi, I want to learn how to calculate the measurements of the yellow board. That being the angle at #1 and where the litte cutout in the board will be at #2. Its not important that the cutout vertical height has to be 2cm, but Im assuming it has to…
Pontus
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How to convert degrees minutes seconds to hour minutes seconds (and viceversa)?

I'm reading the book "Practical Astronomy with your Calculator or Spreadsheet 4th Edition" and I want to implement formula 22: Converting between angles expressed in degrees and angles expressed in hours. It says that: To convert between angles…
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Finding a point on a rounded rectangle using an angle

I'm writing an application where I need to be able to plot points onto a rounded rectangle. I know the angle from the center from 0 degrees to where the point needs to be. I need to know the x and y coordinates of where a line from this angle would…
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Powers of Angles

Is the definition of multiplication extended to include the product of actual angles? For instance, is there any sensible relation between or is there even a notion of things like (for an angle like a radian $R$) $R^3,R^2,R,1,$ and $\frac{1}{R}$ (or…
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Calculate angle from accelerometer on a moving axis

For the purpose of this question, let's say that I have an accelerometer that is on a foot of a human. ( red square on by the heel in the below photo ) I'd calculate the angle the following way, as the leg goes from step 1 to step 2. $\theta =…
angryip
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Angle between two lines/vectors (both magnitude and sign)

Difference in angles for 4 cases Attached figure shows small part of bigger problem. The circle of radius 5 is divided into 4 segments. Midpoints of these segments are marked (e.g. O). From the midpoint of segments, the end points of segment of…
ltxEnthu
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Calculate the angle of a line given a point (x,y) and a slope

Given a point (x,y) and a slope (m), how can I calculate the angle from the x axis. I can calculate the x intercept (x',0) to get a line from the x axis, but I don't know if I am on the right track. In the case of a negative slope I suspect that the…
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How to know where to turn this vector

I have well defined position of an orange vector. Suppose I have two other vectors (blue in the image), how can I know where to turn my orange vector in order to get the same orientation as the blue vectors? I dont want to know how much I have to…
Samul
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Find the angle between vectors

Parallelogram constructed on the vectors $a=5p-2q$, $b=3p+2q$, $|p|=2$, $|q|=3$, $(p\wedge q)=120^{\circ}$. $\sin(a\wedge b)=???$
Maria
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Calculating azimut from latitude-longitude couples

I am trying to develop a program for my ship in order to be able to know what is the azimut of the ships around him. Yet, I don't know how to calculate the azimut given my own position which is the first latitude-longitude couple and the "enemy"…
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Degrees to Grades conversion conceptual doubt

I was reading Loney's book on Trigonometry and had this one doubt. Loney says Since a right angle is equal to 90° and also to 100 g , we have 90° = 100 g . 1 degree = 10/9 grades and 1 grade = 9/10 degress Hence, to change degrees into grades, add…
noobAtMaths
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