https://en.wikipedia.org/wiki/N-sphere
In "Spherical coordinates" section the hyperspherical coordinates are results of arccosinus function. In some other sources there is arccotangent instead:
Whose formulas are correct and whose are an error?
2026-03-26 09:16:18.1774516578
An error in Wikipedia? (trigonometry)
99 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in TRIGONOMETRY
- Is there a trigonometric identity that implies the Riemann Hypothesis?
- Finding the value of cot 142.5°
- Using trigonometric identities to simply the following expression $\tan\frac{\pi}{5} + 2\tan\frac{2\pi}{5}+ 4\cot\frac{4\pi}{5}=\cot\frac{\pi}{5}$
- Derive the conditions $xy<1$ for $\tan^{-1}x+\tan^{-1}y=\tan^{-1}\frac{x+y}{1-xy}$ and $xy>-1$ for $\tan^{-1}x-\tan^{-1}y=\tan^{-1}\frac{x-y}{1+xy}$
- Sine of the sum of two solutions of $a\cos\theta + b \sin\theta = c$
- Tan of difference of two angles given as sum of sines and cosines
- Limit of $\sqrt x \sin(1/x)$ where $x$ approaches positive infinity
- $\int \ x\sqrt{1-x^2}\,dx$, by the substitution $x= \cos t$
- Why are extraneous solutions created here?
- I cannot solve this simple looking trigonometric question
Related Questions in COORDINATE-SYSTEMS
- How to change a rectangle's area based on it's 4 coordinates?
- How to find 2 points in line?
- Am I right or wrong in this absolute value?
- Properties of a eclipse on a rotated plane to see a perfect circle from the original plane view?
- inhomogeneous coordinates to homogeneous coordinates
- Find the distance of the point $(7,1)$ from the line $3x+4y=4$ measured parallel to the line $3x-5y+2=0.$
- A Problem Based on Ellipse
- Convert a vector in Lambert Conformal Conical Projection to Cartesian
- Archimedean spiral in cartesian coordinates
- How to find the area of the square $|ABCD|$?
Related Questions in SPHERICAL-COORDINATES
- Volume between a sphere and a cone
- Trilaterating 2D cartesian coordinates, without Z
- Divergence in Spherical & Cylindrical Polar co-ordinates derivation
- Spherical coordinates to Cartesian coordinates with arbitrary origin for spherical coordinate system
- Triple integral. Spherical coordinates. Too much calculations
- Finding the kernel of a linear map gotten from a linear map with one kind of bessel function $j_i$ and replacing them with the $y_j$
- Distribution of correlation of fixed vector on vectors of n-sphere
- Calculate $\int_{\mathbb R^3} x_3^2 e^{-\lVert x \rVert _2} \lambda_3(dx)$
- Magnitude of a Vector in Spherical Coordinates with No Radial Component
- Rotate the surface of a sphere using altitude
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
It looks like they're the same.
The "arccosine" formula uses the ratio of the $i$th coordinate to the distance from the origin, whereas the "arccotangent" formula uses the ratio of the $i$th coordinate to the length of the projection of the radius onto the plane spanned by the other axes.
That is, notice that all the denominators are the same in the arccos formula, but not in the arccot formula.