# Tagged Questions

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### Finding true bearings?

What is the true north bearing of NNE on 16 point cardinac compass? I just wanna know that is there any exact bearing or do we have to only give an approximate bearing?
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### How do I multiple these matrices together?

As a personal brain exercise, I've recently been trying to work out the math involved with rotating vertices around an arbitrary axis in 3D space. To do so, I've been relying very heavily on the ...
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### Obtaining consistent triangle surface normals.

I am given 3 points in a random order like so... calculateSurfaceNormal(point1, point2, point3); I have implemented the method by simply saying... ...
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### How do I calculate the inverse of these matrices?

In learning how to rotate vertices about an arbitrary axis in 3D space, I came across the following matrices, which I need to calculate the inverse of to properly "undo" any rotation caused by them: ...
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### How to properly sort a set of axis-aligned boxes so they are drawn correctly under this projection?

Given a set S of axis-aligned, non-overlapping boxes {x,y,z,w,h,l}, where x,y,z are their center-positions and w,h,l their width, height and lengths, and given the following orthographic projection: ...
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### Matrix; Linear transformations

Let $( x , y )$ be the co-ordinates of a point P referred to a set of rectangular axes $OX$, $OY$. Then its co-ordinates ($x^{'}$,$y^{'}$) referred to $OX^{'}$, $OY^{'}$, obtained by rotating the ...
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### Order of operations in rotation matrix notation.

I'm trying to convert this equation to C# but I'm not a mathematician and I find math notation ambiguous: See the first matrix in this article: http://mathworld.wolfram.com/RotationMatrix.html ...
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### Use a matrix or equations to find the value of $\sin(\pi/3)$

I was asked to use $\sin(0)=0$, $\sin(\pi/2)=1$, and $\sin(\pi)=0$ to calculate the value of $\sin(\pi/3)$ using matrices or equations. I honestly have no idea how to solve this.
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### matrix representation of a trigonometric rotation

Hey guys!I have a couple of doubts regarding this exercise, for a) I think that the Matrix rotation of P is [(cos t, -sen t) , (-sen t, cos t)] and for Q [(-cos t, -sen t), ( sen t, cos t)] , is ...
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### How to find the exact value of $\cos(36^\circ)$?

The problem reads as follows: Noting that $t=\frac{\pi}{5}$ satisfies $3t=\pi-2t$, find the exact value of $$\cos(36^\circ)$$ it says that you may find useful the following identities: ...
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### Rotating a line segment in 3D to a prescribed orientation

I have a general line segment with endpoints $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$ referenced to a 3D Cartesian coordinate frame E. I wish to rotate this coordinate fram E to a new coordinate system F ...
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### Vector Math and Directional Vectors

Short and sweet. How does one calculate a directional vector in 3 dimensions by knowing the magnitude of the vector and the rotations about both the x and y axis?
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### Angle Between Pair of Vectors

Find the angle $\theta$ between the pair of vectors u and v. $u = \begin{bmatrix} 1\\ 1 \end{bmatrix}, v = \begin{bmatrix} 7\\ 11 \end{bmatrix}$ I already figured that I'll need the ...
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### Linear Algebra - Linear Transformations

Let $V$ be the space spanned by the two functions $\cos(t)$ and $\sin(t)$. Find the matrix $A$ of the linear transformation $T(f(t)) = f''(t) + 7f'(t) + 4f(t)$ from $V$ into itself with ...
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### Finding the position of a point after rotation: Why is my result incorrect

I am attempting to calculate the position of a point after it has been rotated I have been using an algorithm but I am getting incorrect values which makes me think I am using the incorrect algorithm ...
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### Find 3D rotation vector and angle to transform a rectangle into a given quadrilateral

I have a given rectangle that I need to transform into a given quadrilateral shape that resulted from a rotation and translation in 3D space, and subsequent projection. ...
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### $\sin(A)$, where $A$ is a matrix

If $A$ is an $n\times n$ matrix with elements $a_{ij}$ $i=$i'th row, $j=$j'th column. Then $e^A$ is also a matrix as can be seen by expanding it in a power series.Is $e^A$ always convergent and ...
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### Equality of matrix of trigonometric functions in n-power

Could you help me please and give some tips on how should I start solving this problem. How can one prove, that this equation is right, when n from $\mathbb{Z}$ and $\alpha$ is from $\mathbb{R}$? ...
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### Solving an equation with trig functions and two different angles

I am trying to solve this equation derived from matrix multiplication (where $a,b,c,d$ are constants): -a \cos(\theta) \sin(\alpha)-b\sin(\theta) ...
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### How to create 2x2 matrix to rotate vector to right side?

I have vector u=(x,y) and i need to create matrix M: M*u=(1,0). But that matrix has to rotate vector, instead of keep and ...
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### Algebraic proof of a trig matrix identity?

I'll put the question first, and then the background, because I'm not sure that the background is necessary to answer the question: I have a geometric proof, but is there an elegant algebraic proof ...
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### How does multiplying by trigonometric functions in a matrix transform the matrix?

I found this comic: But I can't understand the humor because I can't understand how trig functions affect matrix multiplication. Can someone please explain?
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### Compute Altitude and Azimuth using either Quaternions or Rotation Matrix or Roll, Pitch and Yaw component

I am struck with a mathematical problem. I want to convert the iPhone device's attitude information which is available in one of the following forms: Quaternion Rotation Matrix Roll, Pitch and Yaw ...