# Tagged Questions

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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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 ...
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### 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) = ...
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### 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
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### 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, ...
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### 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 ...
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### 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 ...
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### 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. ...
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### 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 ...
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### 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 ...
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### 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. ...
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### 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 ...
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### 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$cos3x$: $3+\sqrt3tan3x=0$ $tan3x=-\dfrac{3}{\sqrt3}$ $\therefore$ ...
39 views

### Simple Trigonometry and algebra

If $$\sec\theta = X + \frac{1}{4X},$$ then what is $${\sec\theta + \tan\theta}$$ in terms of $X$?
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 ...
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, ...
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### 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 ...
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### 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 $F_1$ ...
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### 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 ...
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### 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? ...
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### Some weird system of equations.

How do you solve this type of system of equations? The unsubscripted variables are to be found. $A^2+B^2={C_1}^2$ $C^2+D^2={C_2}^2$ $E^2+F^2={C_3}^2$ $(A+C)^2+(B+D)^2={C_4}^2$ ...
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### 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 ...
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### 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 ...
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### 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 : ...
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### 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 ...
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### Signed angle between 2 vectors?

http://stackoverflow.com/questions/2150050/finding-signed-angle-between-vectors on this link I found the following formula: ...
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### 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 ...
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### 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 ...
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### 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 ...
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*} ...
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 ...
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### 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 ...
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 ...
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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 ...
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 ...
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 $R$. ...