0
votes
0answers
21 views

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?
0
votes
1answer
47 views

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 ...
0
votes
1answer
14 views

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... ...
0
votes
2answers
38 views

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: ...
1
vote
0answers
21 views

Rotating two objects

I have two lines. Both created in this format: Line 1 $$line1 = \left\{ \begin{array}{c} startX, startY \\ endX, endY \end{array} \right\}$$ $$line2 = \left\{ \begin{array}{c} startX, startY \\ endX, ...
0
votes
1answer
73 views

Quaternion isn't normal!

I use the following scheme: Quaternion: [ w, x, y, z ] Then I use Euler Angles and convert it to a quaternion, as following: ...
0
votes
3answers
135 views

Compute the determinant $\begin{vmatrix} \sin x & \cos x \\ -\sin y & \cos y \end{vmatrix}$ using the Sarrus' rule

I have an exercise that asks to compute the determinant using the rule Sarrus $\begin{vmatrix} \sin x & \cos x \\ -\sin y & \cos y \end{vmatrix}$ The rule is not just for Sarrus $3\times 3$ ...
2
votes
2answers
143 views

How to calculate the determinant of this matrix $A=\begin{bmatrix} \sin x & \cos^2x & 1 \\ \sin x & \cos x & 0 \\ \sin x & 1 & 1 \end{bmatrix}$

How to calculate the determinant of this matrix $A=\begin{bmatrix} \sin x & \cos^2x & 1 \\ \sin x & \cos x & 0 \\ \sin x & 1 & 1 \end{bmatrix}$ ...
0
votes
0answers
278 views

Matrix with trig functions and Cramer's rule

Using Cramer's rule solve for $x'$ and $y'$ in term of $x$ and $y$ $x = x'\cos\theta - y'\sin\theta\\ y = x'\sin\theta + y'\cos\theta$ So what I have is this $\det\begin{bmatrix} \cos\theta& ...
1
vote
2answers
181 views

I've seen “hyperbolic rotation” - from this: generalization to multisection rotation: is this possible?

This question is more in recreational mathematics area By accident I came across the concept of "hyperbolic rotation" where we use a matrix containing $\cosh$ and $\sinh$ instead of the ...
0
votes
0answers
20 views

Resolving bearings for tilted structure (vector rotations)

I am trying to find a neat solution to resolving bearings for a tilted structure. For example, if I know that a hub is $268.74^{\circ}$ and offset ($X = -3.542 $m, $Y = -1.857$ m, $Z = 2.013$m) with ...
0
votes
0answers
162 views

Converting a 3x3 matrix to euler angles in various rotation orders

So let's say I have a 3x3 orientation matrix set up like: a b c d e f g h i which I have generated from euler angles in a left-handed, Y-vertical system. ...
0
votes
1answer
54 views

Using a matrix vector product to show a specific example

I am suppose to use a matrix vector product to show that if $\theta$ is 180 degrees then $A_\theta v = -v$ for all v in $R^2$ I have no idea what this means and it is really confusing, as far as I ...
2
votes
6answers
679 views

why is the square of this matrix with sin and cos equal to the identity matrix?

I have a question about why the square of the matrix Q, below, is equal to the identity matrix. Q = cos X -sin X sin X cos X My knowledge of ...
3
votes
4answers
164 views

$4^\text{th}$ power of a $2\times 2$ matrix

$$A = \left(\begin{array}{cc}\cos x & -\sin x \\ \sin x & \cos x\end{array}\right)$$ is given as a matrix. What is the result of $$ad + bc \text{ if } ...
1
vote
1answer
36 views

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: ...
0
votes
2answers
66 views

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 ...
7
votes
1answer
309 views

Eigenvalues of a tridiagonal trigonometric matrix

Let $A$ be the diagonal matrix w/alternating in sign diagonal entries: $$ A = \begin{pmatrix} (-1)^{n-1} \tan\left(\frac{\pi}{2n+1}\right) & 0 & 0 & \ldots & 0 \\ 0 & ...
10
votes
2answers
321 views

A matrix w/integer eigenvalues and trigonometric identity

Any intuition and/or rigorous arguments on the proofs of the following statements would be appreciated: Let $n$ be a natural number. (a) Consider the following Toeplitz/circulant symmetric matrix: ...
7
votes
3answers
361 views

How to find the eigenvalues and Jordan canonical form of this matrix

Question: let $a_{i,j}\in R,A=(a_{i,j})_{n\times n} $,and $a_{i,j}=\begin{cases} 1&i+j\in\{n,n+1\}\\ 0&i+j\notin\{n,n+1\} \end{cases}$ that's meaning: $$A=\begin{bmatrix} ...
1
vote
3answers
201 views

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 ...
1
vote
2answers
114 views

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.
-1
votes
3answers
181 views

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 ...
4
votes
6answers
667 views

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: ...
1
vote
1answer
206 views

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 ...
0
votes
1answer
106 views

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?
1
vote
1answer
1k views

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 ...
0
votes
2answers
1k views

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 ...
0
votes
1answer
1k views

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 ...
1
vote
1answer
581 views

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. ...
14
votes
5answers
2k views

$\sin(A)$, 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 ...
2
votes
2answers
324 views

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 $\mathbb{R}$? ...
1
vote
1answer
526 views

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) ...
3
votes
3answers
641 views

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 ...
10
votes
2answers
750 views

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 ...
14
votes
4answers
990 views

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?
0
votes
0answers
2k views

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 ...