2
votes
1answer
30 views

For what $n$ the set $\{\sin x, \cos x, (\sin x)^2, (\cos x)^2,…, (\sin x)^n, (\cos x)^n\}$ is linearly independent?

Under what condition of $n$ the following set $\{\sin x, \cos x, \sin^2x, \cos^2x,..., \sin^nx, \cos^n x\}$ is linearly independent? I tried to replace n=1,2,3 but I haven't get the general result. ...
0
votes
1answer
66 views

Are Euclidean distances a monotone function of inner products?

Does the sum of all pairs of inner-products of k vectors (real) have to decrease if the sums of Euclidean distances between all pairs of $k$ vectors happens to decrease? Similarly-if decrease is ...
0
votes
2answers
41 views

Show that the functions are vectors.

Let $V$ be the subspace of $C^1(\mathbb R)$ spanned by $f(x) = \sin x $ and $g(x) = \cos x$. a) Show that for any constant value of $\theta$, the functions $f_1(x)=\sin (x+ \theta) $ and $f_2(x)= ...
1
vote
0answers
65 views

independent/dependent values at different frequencies and phases

I am curious about the following problem. I would like to ask for help solving it. Consider the following $m$ sinusoidal functions $\sin(\omega_{1}⋅t+\phi_1),\sin(\omega_{2}⋅t+\phi_2),..., ...
1
vote
2answers
46 views

What is wrong with this basic algebra/trig that I'm doing?

I have to solve for $x$: $e^{x\sqrt3}(3cos(3x)+\sqrt3sin(3x))=0$ So $3cos3x+\sqrt3sin3x=0$ Divide through by$cos3x$: $3+\sqrt3tan3x=0$ $tan3x=-\dfrac{3}{\sqrt3}$ $\therefore$ ...
0
votes
3answers
36 views

Simple Trigonometry and algebra

If $$\sec\theta = X + \frac{1}{4X},$$ then what is $${\sec\theta + \tan\theta}$$ in terms of $X$?
0
votes
1answer
47 views

converting a signal back and forth with trigonometric functions

I'm trying to convert a signal back and forth using trigonometric functions. In the example below: 1) start off with a cos signal 2) convert the signal to a secant signal 3) would like to convert ...
2
votes
3answers
106 views

Find radius of a circle which is tangent to three known lines

I need to find the equation for a circle which is tangent to the following three lines: y=0 x=0 y=-x+0.338334 For the last tangent line equation, I know that it is tangent at the point (0.169167, ...
0
votes
1answer
60 views

Linear algebra or trigonometry? [closed]

Im currently learning game development but math is preventing me to go farther. So i decided to take a course in khan academy. But im kinda confuse, Should i take trigonometry first or the linear ...
0
votes
1answer
28 views

Determining some vectors.

I'm having a very difficult time with this problem. The mast $CD$ is kept in balance by two wires which form the angles $\alpha$ and $\beta$ with the horizontal plane. The length of the vector $F_1$ ...
2
votes
1answer
31 views

How do I calculate the intersection between two cosine functions?

$f(x) = A_1 \cdot \cos\left(B_1 \cdot (x + C_1)\right) + D_1$ $g(x) = A_2 \cdot \cos\left(B_2 \cdot (x + C_2)\right) + D_2$ Is it possible at all to solve this analytically? I can start ...
1
vote
0answers
63 views

How to calculate center coordinates of two reverse arcs in 3D space

Given 3D points P1(200,60,140), P2(300,120,110), P3(3,0,-1), P4(-100,0,-1) and the radius of arc C1MP3 is equal to radius of arc C2MP1. How do I calculate coordinates x, y, z of points C1 and C2? ...
4
votes
1answer
94 views

Some weird system of equations.

How do you solve this type of system of equations? The unsubscripted variables are to be found. $A^2+B^2={C_1}^2$ $C^2+D^2={C_2}^2$ $E^2+F^2={C_3}^2$ $(A+C)^2+(B+D)^2={C_4}^2$ ...
0
votes
1answer
73 views

Converting from spherical coordinates to cartesian around arbitrary vector $N$

So if I'm given an arbitrary unit vector $N$ and another vector $V$ defined in spherical coordinates $\theta$ (polar angle between $N$ and $V$) and $\phi$ (azimuthal angle) and $r = 1$. How do I ...
1
vote
1answer
46 views

Unit circle - how to prevent backward rotation

Let's assume we have a unit circle (0, 2$\pi$). Basically I have a point on this circle who is supposed to move only forward. This point is controlled by the user mouse and constantly calculate 25 ...
0
votes
0answers
138 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
44 views

Make the vector $[1,1]$ turn of an angle - $\pi/4$ , with complex numbers

We have $[1,1]$ and $\theta = -\pi/4$ here is my attempt: $(\cos(-\pi/4) + i \sin(-\pi/4)) * (x+iy)$ = $(\sqrt{2}/2 - i \sqrt{2}/2) (1+i)$ = $\sqrt{2}/2 - i^2\sqrt{2}/2 $ = $[\sqrt{2}/2 + ...
1
vote
0answers
89 views

How to solve a hard trigonometric equation

I have come across a trigonometric equation which I need to solve, $(B+2A\cos(2x+\theta))(2\sin x|\cos (2x+\theta)|-\cos x )+2A\sin x \sin(2x+\theta)|\sin(2x+\theta)|=0 $ $A,B$ and $\theta$ are ...
0
votes
1answer
65 views

Signed angle between 2 vectors?

http://stackoverflow.com/questions/2150050/finding-signed-angle-between-vectors on this link I found the following formula: ...
0
votes
2answers
64 views

Prove the identity

$$\cos \frac{x}{2} \cdot \cos \frac{x}{4} \cdot \cos \frac{x}{8} = \frac{\sin x}{ 8\sin \frac{x}{8}}$$ Conjecture a generalization of this result and prove its correctness by induction. Ps: I have ...
-1
votes
2answers
75 views

Two objects travel on a 2 dimensional grid. How can i find the angle that must be taken in order for the interception time to be the smallest [closed]

An object (a) travels on a linear path at constant speed. A second object (b) must intercept object a in the shortest amount of time possible. Object b is also at a set speed and can travel in any ...
0
votes
1answer
49 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
577 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 ...
0
votes
0answers
85 views

How to Find End Point, after rotation

I am having an 3D object, length of the object is 27.5 meter, rotation value is -30 degree and the rotate origin point will be one end. After rotating the object i want to find the coordinate of ...
1
vote
3answers
265 views

Velocity vectors and trigonometry

I am trying to learn about velocity vectors but this word problem is confusing me. A boat is going 20 mph north east, the velocity u of the boat is the durection of the boats motion, and length is ...
3
votes
4answers
163 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
34 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: ...
1
vote
0answers
115 views

Determining similarity between paths (sets of ordered coordinates).

With limited knowledge of mathematics, I am not sure what tags to use for this question. I have a path on a 2D surface called $(p1)$. A path consists of a set of ordered $(x,y)$ coordinates. By ...
0
votes
2answers
97 views

Orthogonality of eigenvectors of laplacian

Let $x_i=(\sin i\pi/n,\cdots,\sin (n-1)i\pi/n)$ for $i=1,\cdots,n-1$. I want to show that $x_i \cdot x_j=\delta_{ij} n/2$. Why is it true? I tried $\sin a \sin b=-[\cos(a+b)-\cos(a-b)]/2$ but don't ...
0
votes
3answers
189 views

Solve system of equations involving cos and sin

I have come up with the following system, I want to solve it for $a$ and $c$: $ a \sin (x_0) - c \sin(x_0 - L) = 0\\ c \cos(x_0 - L) - a \cos(x_0) = 1 $ In this system $x_0$ and $L$ are arbitrary. ...
17
votes
2answers
360 views

Angular distribution of lines passing through two squares.

Let's say I've got two squares with side length $d$ that are held parallel at a distance $m$ apart. Suppose that particles are randomly falling from above in such a way that the polar angle ...
7
votes
1answer
290 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 & ...
2
votes
1answer
816 views

How to Find the Center of a Parallelogram

I want to find the center of a parallelogram in order to use it in my java program. I have four coordinates of the parallelogram and I want to find the center coordinate of the parallelogram. It seems ...
4
votes
1answer
73 views

Optimal rotation to align a circle with external points

I have a circle $C$ with radius $r$ and a set of finite points $P=\left \{ p_1,p_2,\ldots,p_n \right \}$ are identified external to the circle $C$. These points may lie on the exterior or the interior ...
1
vote
1answer
36 views

Angle consistency between vectors in N dimensions

I am trying to understand how rotations work in higher dimensions. Let us assume we have a set of points $p_i\in P$ in $N$ dimensions, related to another set of points $q_i \in Q$ by a rotation $R$. ...
0
votes
2answers
25 views

Magnitude of Axis vectors in question

I have a question on my revision sheet: Write the vector, v=-2 i + 4 j , in polar form. is it safe to assume axis vectors i and j have a magnitude of 1?
7
votes
3answers
352 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
0answers
53 views

Pure Phase Number

I am read a solution (4.9) Here say: ... both $a, d$ are pure phases, so that it is always possible to find (non unique) real numbers $\alpha, \beta, \delta$ such that $a = ...
0
votes
1answer
80 views

What is required to establish the law of cosines?

In my quantum computation course, we have been given nothing more than the basic axioms of a linear vector space, and and the properties of an inner product; but we have started referring to "the ...
7
votes
2answers
97 views

Find eigenspaces using ruler and compasses

I think this is an interesting question: In the 2-dimensional real vector space, we are given a linear transformation $f$. Suppose we already know the images of the standard bases, say ...
2
votes
2answers
82 views

Duplicate quadratic Bézier curve with new start point?

I have Bézier curve as shown by the wikipedia gif here: I would like to create a new curve that is a segment of the old one. For example, in this gif (from the same article): .. if I wanted B to ...
1
vote
3answers
177 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 ...
2
votes
4answers
552 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: ...
3
votes
1answer
79 views

Check If a point on a circle is left or right of a point

What is the best way to determine if a point on a circle is to the left or to the right of another point on that same circle?
3
votes
1answer
1k views

Explanation of this image warping (bulge filter) algorithm

I've been researching image warping algorithms lately and haven't found many comprehensive references. That said, there are of course code snippets from GIMP, jhlabs.com, and imagemagick.org but none ...
0
votes
1answer
98 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?
3
votes
3answers
1k views

How to figure out the Argument of complex number?

I have the absolute value of complex number , $$ r = |z| = \sqrt{x^2 + y^2}$$ when $z = x + iy$ is a complex number. How can I calculate the Argument of $z$? Thanks.
1
vote
1answer
80 views

Vector / trigonometry question

I'm checking out this programming tutorial on raycasting at http://lodev.org/cgtutor/raycasting.html and have a probably very simple question about the math used. I'm having trouble understanding the ...
1
vote
1answer
102 views

How is the dotproduct a projection?

I don't understand who projects on who. How is the following a projection on anything? I don't see how a vector of lenght 6 can possibly result of a projection here. If I project C down to the x-axis, ...
0
votes
1answer
94 views

find the multiplicative factor for get a specific amount of sum on sin

i am not a math guru so please sorry if this is a silly question. i'm not sure on how to latexize this question so i've done a spreadsheets with openoffice (and i'm interest also in the best way to ...