1
vote
1answer
25 views

Diff. Eq. Example with Matrices

I'm currently working on a side project of mine that deals with $\sin(A)$ and $\cos(B)$, where $A,B\in\mathbb{C}^{nxn}$. I'm trying to find some interesting (or non-interesting) examples where one ...
1
vote
1answer
23 views

How could I calculate the local size of an object given its distance and actual size?

Lets say I take a picture of a sign. I know that sign is 20ft (width), 10ft height. I'm standing 40 feet away. If I were to take a picture, how could I calculate how wide and how high the sign is in ...
1
vote
3answers
64 views

Find a basis of $A = (\{1, \sin(x), (\cos)^2(x), (\sin)^2(x)1\})$ and determining its dimension.

We consider a space F(R,R) of functions of R in R. Let A = ({1, \sin(x), $\cos^2(x)$, $\sin^2(x)$}) Find a basis of the vector subspace of F(R,R) and determine its dimension. So I used the identity ...
1
vote
1answer
16 views

Calculating amount of rotation to straighten an imaginary line created by 2 points.

I am trying to build a small app where my users can straighten up a tilted face with just 2 clicks I ask my users to click on the middle of the nose and the middle of the eyebrows of the face ...
0
votes
0answers
32 views

Using Algebra with Trig Functions

Using Algebra with Trig Functions I'm trying to find the correct 1 second audio signal I would need to apply to a 1 second known noise signal to have the output signal be a sin wave. The basic ...
0
votes
0answers
37 views

inverse of function with sine mooculus

I'm trying to do a calculus course on line: mooculus and I'm trying to answer this question: The height in meters of a person off the ground as they ride a Ferris Wheel can be modeled by h(t) = ...
0
votes
1answer
31 views

Find points near end point of a line

Any equation to find points near to both start and end points of lines with different slopes. See image. Need P and Q. If Endpoints are named A and B, AP and BQ should be 1 cm
0
votes
1answer
67 views

How to determine the visibility of an object from the top of a hill

We are developing software to train children how to cross the street safely. Part of the training is to teach them not to cross when they don't have enough visibility due to obstacles. In this case, ...
-1
votes
2answers
35 views

How to solve $\frac12 \sec^2 \frac x2 = 1$ under restricted domain?

solve: $$\frac12 \sec^2 \left(\frac x2\right) = 1$$ and domain $x: (-\pi,\pi) \cup (\pi,3\pi)$. sec^2 (x/2) = 2 sec^2 (x/2) can be re-written as tan(x/2)^2 + 1, therefore tan^2(x/2) + 1 = 2 ...
0
votes
1answer
31 views

General Solution for Cosine (negative angles)

cos2(x+pi/3)=1/2 2(x+pi/3)=pi/3 x+pi/3=pi/6 x+2pi/6=pi/6 x=-pi/6 x=5pi/6 (is this step correct) ... ?? x = +/- pi/6 +kpi , k is a subset of Z x = +/- 5pi/6 +kpi , k is a subset of Z can someone ...
0
votes
1answer
19 views

Localizing a point using distance measurements to four points in 3-D

This article explains how to do trilateration step by step. I need to extend this process to 3-D. As far as I know, I need four distance measurements in order to calculate a fifth point's coordinates. ...
1
vote
2answers
59 views

Rotate $z = 0$ plane in 3D

I have 100 points on $z=0$ plane. I want to rotate those points, such that they lie on any plane $P(a,b,c,d)$, preserving distances. Hence, I need a rotation matrix. For instance, if my points are ...
1
vote
0answers
39 views

How to approach sketching sine and cosine graphs with transformations

Any tips or suggestions in sketching these graphs quickly, and in ONE go? In exams, I don't want to spend ages re-drawing the original sine/cosine graph, one by one, following each new ...
2
votes
1answer
33 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
106 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
47 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
48 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
39 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
58 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
171 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
99 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
29 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 $F_1$ ...
1
vote
1answer
37 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
88 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
107 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
96 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
52 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
1answer
51 views

Find $k$ such that the angle between the vectors $(2,k)$ and $ (3,5)$ is $60$ degrees

I have $2$ vectors : $U =(2,k)$ and $V = (3,5)$. I want to find the $k$ value when the angle between $U$ and $V$ is $60$ degrees. This what I tried to do but I don't get the right answer : ...
0
votes
0answers
297 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
184 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
84 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
71 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
84 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
57 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 ...
3
votes
1answer
300 views

Why n! equals sum of some expression?

Why n! equals sum of some expression? Especially I need to know why this expression is true? $$ n!= \left(\frac{n+1}{2}\right)^{p(n)} \; \prod_{j=0}^{q(n)}\sum_{i=0}^j(n-2i), $$ Where \begin{gather*} ...
2
votes
6answers
700 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
91 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
435 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
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
37 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
145 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
101 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
223 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
376 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
310 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
1k 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
80 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
49 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 $R$. ...