Trigonometric functions (both geometric and circular), relationships between lengths and angles in triangles, and other topics relating to measuring triangles.

learn more… | top users | synonyms (1)

5
votes
1answer
79 views

How to find inverse of $\sin(x) + \sin(2x) = y$?

I was wondering if there were any way to solve the equation $$\sin(x) + \sin(2x) = y$$ in terms of $x$. This of course would allow us to express the inverse for this function on $-\frac{\pi}{4}$ to ...
4
votes
1answer
162 views

Radical expression for Cosine formulas

Is there nice radical expression for $$\cos\left(\frac{\pi}{2^k+1}\right)?$$ Example: $\cos\left(\dfrac{\pi}{5}\right)=\dfrac{\sqrt{5}+1}{4}$. Please provide some concrete examples. Also please ...
0
votes
0answers
280 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& ...
0
votes
0answers
30 views

Help solving a function

I have $2$ equations and $2$ angels that i need $V_{1}$ and $V_{2}$. I know The Point $(X_{m}, Y_{m})$ and the point $(X_{a}, Y_{a})$. I have one point $(X_{p}, Y_{p})$ that moves with the equation ...
0
votes
0answers
75 views

Help me debunk mathematically a driving law.

I was wondering if you guys can assist me calculating the relative probability of an accident scenario given the following info. Disclaimer: What we will look at now is just a "model" or a ...
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
58 views

Linearising angle to chord length over a reasonable domain of < pi; or, how to make measuring a rock with a protractor easy

Imagine that I have a protractor and compass, and wish to use it to measure the distance between two points (potentially in three dimensional space, such as on a rock). However also being a forgetful ...
0
votes
0answers
381 views

Sum of Sinusoids with Same Frequency = Sinusoid (proof)

I am studying Fourier analysis on my own, I realised that probably the first thing you want to proof in Fourier transform is that the sum of 2 sinuoids (namely a sine and cosine) with the same ...
0
votes
0answers
163 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
0answers
44 views

Triangle ABC. 3rd point.

I have a triangle ABC, xyz coordinates of points A and B are known. Also, length AB, AC and BC are known. How can I get the xyz coordinate of point C with respect to the xyz frame?
0
votes
0answers
26 views

Find vector with simple trigonometry

I've spent too much time solving a fluid mechanics problem because of this trigonometry. How do I find $V_{t2}$ ? The answer is $rw - V_{n2} \cot(\theta)$. (can't seem to get equations to work)
0
votes
0answers
85 views

Product of Sinusoids: Sum of Frequencies (proof)

In this article: http://en.wikipedia.org/wiki/Negative_frequency#Applications they write: "the product of two complex sinusoids is also a complex sinusoid whose frequency is the sum of the original ...
0
votes
0answers
20 views

Is it possible to find an exact expression for system for recursion of non linear equations?

I have a system of N non-linear equations of N unknowns $\phi_i, i \in 1,2,... N$. By specifying the middle two unknowns as $\phi_{N/2} = 0, \phi_{N/2+1} = X$, I get that: \begin{align*} ...
0
votes
0answers
16 views

Parametrically defined Spheres in $R^n$

So I have 2 questions here which are closely linked: How do you parametrically define the circle $(x')^2 + (y')^2 = r^2$ using (x') and (y') as coordinates on the plane ax + by + cz = 0 that are ...
0
votes
0answers
179 views

Law of cosines on cyclic quadrilateral

‎Consider‎ the ‎triangle ‎$\triangle‎‎ ABC$ ‎with‎ ‎area‎ $n$. Let $a$ denote the lenght of side $A$; and similarly with $b$ and $B$; $c$ and $C$. Denote ‎$\theta$‎‎ as the measure of angle ...
0
votes
0answers
90 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 ...
0
votes
0answers
107 views

Trying to find coordinates of another point using bearings

I am trying to help one of my siblings with a trig project and there is one part that I am having a little trouble with. In his project, he is trying to find the coordinates of a UFO given the ...
0
votes
0answers
68 views

Prove the Lobachevsky-Bolyai formula for the Klein model

I want to prove that e^(-d) = tan(Π(d)/d) in the Beltrami-Klein Model for the angle of parallelism in correspondence to the distance d, where d is the klein distance d(AB) = (1/2)|ln((AB,PQ)). A hint ...
0
votes
0answers
64 views

Spherical clipmap to heightmap mapping

I'm working on a library to create real time rendered planet models using spherical clipmaps. I can't seem to figure out how to map my heightmaps to the clipmaps and was hoping someone here could ...
0
votes
0answers
16 views

Trigonometry; How do we derive the result for B $(x^{'},y^{'})$ from A $(x,y)$?

Let A $ ( 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 ...
0
votes
0answers
69 views

Get the entrance point from a straight line in a rectangle

The rectangle is like a street. The right half is to go upwards, the left half to go down. The red lines are paths of vehicles. And my goal is to give every vehicle the right lane. So when you look at ...
0
votes
0answers
99 views

Getting the angle between three points

So I have this psuedo code here (converted from c# to show you better) ...
0
votes
0answers
82 views

What is this expression called?

Could anyone please tell me if they recognize this equation? What it does is calculate the angle between two lines, but I need it's name. Any help is greatly appreciated! $$\sin \theta = A_{1} \cdot ...
0
votes
0answers
80 views

Any obvious simplification of sin(x) / sin(y)

I have an expression that is made up of the sines of several angles unfortunately none of them are "friendly" angles such as 60 or 45 but sine occurs several times. I get the feeling there might be ...
0
votes
0answers
888 views

General solution of trigonometric function

For any real numbers $x$ and $y$. $\sin x = \sin y \implies n\pi + (-1)^ny, $ where $n \in Z$ If $\sin x = \sin y$, then $\sin x -\sin y = 0$ or $2\cos\frac{x+y}{2}\sin \frac{x-y}{2} = 0$ ...
0
votes
0answers
73 views

Finding anti derivative

It is mentioned in a different thread that $U(x)=\sin\left(\dfrac1{\ln(1+x^2)}\right)$ is an elementary function. My question is, how do you integrate it then?
0
votes
0answers
72 views

Torus equation in terms of tangent

So if I have an equation for a torus in $F(a,b) = (X, Y, Z)$ where $X = (R + r\cos a)\cos b$ and $0 < r < R$, how would I go about rewriting this equation for $X$ in terms of $\tan(a/2)$ and ...
0
votes
0answers
109 views

A construction of the trig functions on the unit circle

Can anyone shed some light on this picture? http://upload.wikimedia.org/wikipedia/commons/9/9d/Circle-trig6.svg I am not interested in "$\sin$", "$\cos$", or the outdated trig functions. How do we ...
0
votes
0answers
80 views

How would I go about solving this Euler's Equation problem, getting even and odd components?

I'm stuck on this question in my signals and systems class, the question asks to find the even and odd components of the equation. Now I know that $e^{jx} = \cos(x) + j\sin(x)$, however this ...
0
votes
0answers
39 views

Solving for $R$ given $\tan p=\frac{18H}{243-H^2}$ and $R(243-H^2)\cos p+18HR\sin p=1$

Ok so we start with $$\tan p=\frac{18H}{243-H^2}$$ And use this in the equation $$R(243-H^2)\cos p+18HR\sin p=1$$ To find $R$ in terms of $H$ without trig functions I have the answer by the way, ...
0
votes
0answers
73 views

Trigonometry Question

In trigonometry to measure the height or distance of objects we consider the distance between the observer and object to be straight. But the surface of the earth is curved. Assuming the line to be ...
0
votes
0answers
60 views

Rearrange $y = \frac{\tan\left(\frac{N x}{2}\right)}{N}$ to give N

Is it possible to rearrange $$y = \frac{ \tan \left(\frac{N x}{2}\right)}{N}$$ where $x \lt \pi$ as a function of x and y that gives N?
0
votes
0answers
96 views

Reverse Engineering (Inverse?) complex trigonomic function

So, I have this nifty function: ...
0
votes
0answers
132 views

Determining a point in 3D space

So given a point, a rotation around the y-axis, a rotation around the x-axis, and a distance, how can one calculate the relative point in space? For example, the beginning coordinates are (0,0,0). ...
0
votes
0answers
91 views

$\cot(x)$ or $\tan(x)$ amplitude with $F(x)$ or $G(x)$?

If you are doing $f(x)$ and $g(x)$ of a tangent/cotangent function and you get an amplitude. Should you write the final equation with or without the amplitude because technically tan and cot don't ...
0
votes
0answers
267 views

Distance between two objects in a picture

lets say I have a photo that has a picture on a wall and a book upright on the desk. now i know the size of both of these objects. I want to find the distance between two of them on the photo, I was ...
0
votes
0answers
125 views

Calculate distances with Lat and Long

I am trying to calculate a waypoint a set distance away from my current location. I know my Lat and Long of my current location and the distance away a want the waypoint to be. I also know the ...
0
votes
0answers
192 views

Calculate coordinates of the a point in space with hypotenuse and two angles given

I have a cylinder with a length of $2$, and two angles for rotation around two of the axes. Functions for that are named $\text{RotX}$ (rotation around X axis) and $\text{RotZ}$ (rotation around Z ...
0
votes
0answers
41 views

best way to detect the trigonometric identites that shall work on a given expression so as to simplify it accordingly?

how to tell that what trigonometric identity (a.k.a. Pythagorean trigonometric identity) will work on the given equation , so then you can simplify the equation accordingly in order to apply that ...
0
votes
0answers
86 views

Approximating a function with a sine function: transform into constant amplitude?

I have a smooth function, it is stationary. So I tried approximating my function with regression by fitting a sine function that changes period, phase & frequency every observation to get the ...
0
votes
0answers
143 views

Solve this trigonometric system $ \tan x+\tan y=2\sqrt3 \land \tan\frac{x}2+\tan\frac{y}2=\frac{2\sqrt3}3 $

$$ \tan x+\tan y=2\sqrt3 \land \tan\frac{x}2+\tan\frac{y}2=\frac{2\sqrt3}3 $$ I need full solution please. I've tried different transformations, but couldn't get much near, I keep getting huge ...
0
votes
0answers
111 views

Set of all points which are a specified angle away from a given point on a sphere.

I have a sphere with a known point on the surface in polar coordinates. I'm looking to find the set of all points which are exactly some angle away from this point in polar form (this should describe ...
0
votes
0answers
111 views

Sufficient to show that $\sinh(\operatorname{arcsinh}(x))=x$ for arcsinh being the inverse of sinh?

I have to show that arcsinh is the inverse function to sinh. I checked that $\sinh(\operatorname{arcsinh}(x))=x$. Is that sufficient or do I also need to show that ...
0
votes
0answers
179 views

Double integration involving polynomial functions and sinc function

I encountered a problem which I can't seem to simplify/solve. I was wondering if any mathematicians or specialists knows how to approach this problem? $$\int^{0.5}_{-0.5} \int^{0.5}_{-0.5} \; ...
0
votes
0answers
329 views

trigonometry and formula

I asked the same question some time ago, but it is closed. This time I will be clearer (I hope). If I have a right triangle $c ^ 2 = a ^ 2 + b ^ 2$, and $b > a$ (so $a$ is the shorter side and ...
0
votes
0answers
63 views

How can I convert lines intersecting a plane into a focused image?

I am writing a particle transport code. I would like to be able to obtain an image of my geometry when transporting photons given the following information: The photons are incident on a plane. For ...
0
votes
0answers
77 views

Counteract preceding rotations

In a situation where I have two axis adjacent back to back (let's say a robotic arm) I can sometimes perform two rotations ($R_1, R_2$) such that the resulting position and direction is unchanged. ...
0
votes
0answers
221 views

Trig identities for $A\sin^2(x)+\cos^2(x)$

Does anyone know of any useful trig identities for manipulating $A\sin^2(x)+\cos^2(x)$? The only thing I come up with is: $A\sin^2(x)+\cos^2(x)=\frac{1}{2}(1+A)+\frac{1}{2}(1-A)\cos(2x)$ I'm trying ...
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 ...
-1
votes
0answers
36 views

Area between [0, pi/2] of cosine curve (under) using a summation of cossine

Could you help me? I got this formula using Euler's Identity and now I have doubt how to use it. $$\sum_{k=1}^n\cos(k\theta)=\frac{\sin\frac{(n+1)\theta}{2}}{\sin\frac\theta2}\cos\frac{n\theta}{2}$$ ...