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)

1
vote
0answers
171 views

Solving or approximating an equation with radicals and arctan function

I have solved a differential equation recently, which left me with this whopper of inverse function to figure out. I know what $c$ is, I just haven't calculated its exact value based on the initial ...
1
vote
0answers
264 views

Derive trigonometric functions from these equations.

(A) $\sin(-x)=-\sin x$ (B) $\cos(-x)=\cos x$ (C) $\cos(x+y)=\cos x\cos y-\sin x\sin y$ (D) $\sin(x+y)=\sin x\cos y+\cos x\sin y$ Use these equalities to derive the following important ...
1
vote
0answers
1k views

Direction ratio of a vector in 3d?

Suppose I have a vector whose starting end is the origin & the other end can be in any of the 8 quadrants (in 3d). I can easily get direction ratios for the vector & also know in which ...
1
vote
0answers
5k views

A complicated trigonometric equation

I have the following trigonometric equation $$f(\theta)=100(A_2 B_3 - A_3 B_2)^2 - (c_1B_3 - c_2 B_2)^2 - (c_2A_2 - c_1 A_3)^2=0,$$ where: $ A_2 = 3\cos(\theta)-5$ $B_2 = 3\sin(\theta)$ $A_3 = ...
1
vote
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
vote
0answers
238 views

Calculating the Epsilon Neighborhood of line segments in 3d

I am working on a trajectory clustering algorithm (in C++) and one of the steps required in this algorithm is to take a set of 3d line segments (D), and for each line segment (L) in D, to calculate an ...
0
votes
0answers
26 views

how to find trigonometric angle of any value?

how to find value for this- cot(1.3333) in degrees, without using a calculator? if it is possible please explain the process involved and how to find values of other similar questions.
0
votes
0answers
36 views

Trigo Study plan

In what order of topics is probably the most effective in learning trigonometry for starters... where should I first start? and steps in between to De Moivre's Theorem (which is the last topic)... ...
0
votes
0answers
25 views

Making a metric out of distance measure

I'm working with a pseudo-distance measure that is not a metric since it does not hold the triangle inequality. It is called Dynamic Time Warping. The problem is - I need to perform some projections, ...
0
votes
0answers
40 views

Solutions of trigonometric equation $a\sin(x) + b\cos(x) = n$

Is there a solution of the equation $a\sin(x) + b\cos(x) = n$ in rational numbers (i.e. $a,b,n,x$ are rational and positive) where $x$ is not of the form $90n^\circ$? (This question was also there on ...
0
votes
0answers
40 views

Law of Cosines for SSA triangles

In most geometry courses, we learn that there's no such thing as "SSA Congruence". That is, if we have triangles $ABC$ and $DEF$ such that $AB = DE$, $BC = EF$, and $\angle A = \angle D$, then we ...
0
votes
0answers
8 views

Finding common roots to a variable number of functions

I am trying to solve the following problem. Given $a\in\mathbb R^n$, $u\in\mathbb{R}^n$, $m\in\mathbb{N}^\star$, Find the/some common roots $(t_1,...,t_m)$ of the $\frac{m(m-1)}{2}$ ...
0
votes
0answers
12 views

How to determine the period of the following functions?

How would the following make a difference to the period of a function? $$ \cos(t)~~~~ (1)$$ $$ \cos(\omega t)~~~~ (2)$$ $$ \cos(\omega t + \phi)~~~~ (3)$$ Would this be right, $(1)$ has period ...
0
votes
0answers
33 views

As the Moon revolves around the Earth, the side of the Moon that faces the E..

As the Moon revolves around the Earth, the side of the Moon that faces the Earth is partially illuminated by the Sun. These "phases" of the moon are described by a fraction F of a lunar disc. For ...
0
votes
0answers
39 views

How to calculate a person's Latitudinal and Longitudinal location based off of Sun and time

INTRO I remembered hearing about it being possible to calculate a person's position or the position a picture was taken, based on time of day and the position of the Sun, position meaning latitudinal ...
0
votes
0answers
42 views

Is there such thing as a Co-theta?

I plan to make a notation for trigonometry called co$\theta$ An example is that co$\theta$ is equal to 45 and $\theta$ is equal to 45. Co$\theta$+$\theta$=90. In this equation, ...
0
votes
0answers
42 views

Fourier Expressions

In the Fourier series, what are all the ways we can express: $\displaystyle\sin\left(\frac{n\cdot\pi}2\right)$ $\displaystyle\cos(n\cdot\pi)$ I know we can express as $(-1)^{(n+1)}$, and as ...
0
votes
0answers
24 views

Coordinates of a point between two other points with a exact distance from one of them

In this situation, I want the coordinates of the point C, I already know the coordinates of A and B, and the distance D (the distance between A and C). C must be on the A-B segment.
0
votes
0answers
21 views

Weierstrass Trig Substitution Proof

After browsing some topics here, through one post, I discovered the "miraculous" Weierstrass substitutions. However, I can not find a decent or "simple" proof to follow. The simplest proof I found is ...
0
votes
0answers
32 views

Asymptotic analysis of Integrals of powers of sine and their application to intersections of hyperspheres

I am trying to estimate the probability of an event in an algorithm. For simplicity, assume there are two hyperspheres of radius $r$, at a distance $r$ from each other. I am looking to see how the ...
0
votes
0answers
31 views

Using axis coordination to represent rotation matrix instead of angles

Euler angles give us clear matrix for conversion of a vector from car reference $Fr^C$ to earth reference $Fr^E$. If $\vec V$ is a vector in different frames it is represented differently: $$\vec ...
0
votes
0answers
24 views

How to approximate a trigonometric to make less computation complexity

I having a trigonometric function such as $$ p_2(s) = \begin{cases} \frac {1}{(2 \pi)^2}(1-\cos (2 \pi s)), & \text{if $s \le1$ } \\ \frac {1}{2 }(s-1)^2, & \text{if $s >1$ } ...
0
votes
0answers
17 views

Sine and cosine graph transformation

I'm having some difficulties with this question A bike is on a stand such that the highest point of the back wheel is 47 inches above the ground. If the pedal is turned counter clockwise, the back ...
0
votes
0answers
12 views

Why do I get these remarkable wave patterns when I put in the sine of (the coefficient of except 0) for x: y=sin((coefficient barring zero)x)

I saw this inequality grapher on Math Is Fun and when I was playing around with it one time, I got something so remarkable: when you enter the sine of (coefficient barring zero)x, it gives you a wave ...
0
votes
0answers
18 views

finding the formula for a sinusoid given 3 points

I have a sinusoid function, but I don't know the frequency or amplitude. I have 3 distinct points which I know lay on the sinusoid. Is this enough information to derive the sinusoid function? ...
0
votes
0answers
38 views

Why does the graph of $y=\cos 2x+\cos 4x$ look so different from the functions $y=\cos 2x$ and $y=\cos 4x$?

What is $y=\cos 2x+\cos 4x$? and why does its graph look so different from the functions $y=\cos 2x$ and $y=\cos 4x$? I don't understand why this function does not follow the general rule ...
0
votes
0answers
7 views

Change transform matrix for a figure in a sequence?

Here is what I want to do All the drawn figures are rects but each one has its own transform matrix which includes translate, rotate, scale and perspective transforms. I want to transform the left ...
0
votes
0answers
20 views

8 Angles Question: What are solutions with all angles rational multiples of pi?

I don't know how to draw a picture, maybe someone can help. Consider a convex quadrilateral $ABCD$. The 8 angles I'm referring to are the angles made between the diagonals and the edges. Explicitly: ...
0
votes
0answers
25 views

How fast is this dot moving when the angle $θ$ between the beam and the line through the searchlight perpendicular to the wall is $π/6$?

A searchlight rotates at a rate of $4$ revolutions per minute. The beam hits a wall located $11$ miles away and produces a dot of light that moves horizontally along the wall. How fast (in miles per ...
0
votes
0answers
27 views

Dirichlet integral using real Analysis

The teacher made this approach to solve the Dirichlet integral , $$ J_n= \int_0^\frac{\pi}{2} \frac{\sin(2nx)}{\sin x}\:\mathrm{d}x,\quad I_n = \int_0^\frac{\pi}{2} \frac{\sin(2n+1)x}{\sin ...
0
votes
0answers
32 views

Evaluating $ \int \cot^{2} \! \left( \frac{\pi}{\lfloor \log(x) / \log(3) \rfloor} \right) ~ \mathrm{d}{x} $.

How would I evaluate $$ \int \cot^{2} \! \left( \frac{\pi}{\lfloor \log(x) / \log(3) \rfloor} \right) ~ \mathrm{d}{x}? $$
0
votes
0answers
21 views

Cartesian extremities of a 3d segment

I have a segment in 3d space and I want to calculate its extremities. I know the cartesian coordinates (x,y,z) of the segment's middle point, the segment's length L and the segment's orientation using ...
0
votes
0answers
26 views

Exponential to Trigonometric function problem

Here is part of the solution to a fourier series problem involving a rectangular pulse train: I'm following along, and have integrated correctly. But I'm stuck at the second last step - I don't ...
0
votes
0answers
21 views

Invert an Excel function containing the tangent

In the following excel formula: =95*1*1/TAN(RADIANS(M3-(10.3/2.01)))/5280) $M3=2.63715$ and let's say the result of this formula is: $5.508306483$ What would ...
0
votes
0answers
23 views

Parallelogram with vertices 0, Xa, Xb, Xa+Xb (X is matrix, a and b are vectors)

There is a paralellogram with vertices 0, a, b, and a+b, whose area is $34$. What is the area of the parallelogram which has vertices 0, Xa, Xb, and Xa+ Xb, where X = \begin{pmatrix} 3 & -5 \\ -1 ...
0
votes
0answers
47 views

How to draw regular tetrahedron from center?

How to calculate all four points of regular tetrahedron if you have x,y and z for center point and x, y and z axis rotation and size of tetrahedron? I want to write this in java script and this is ...
0
votes
0answers
30 views

Trying to Find Bounds on a Trig Function

I have the function $|\sin(\frac{N+1}{2}x)\sin\frac{Nx}{2}|$ and I want to use inequalities to get it to the form $c\sin\frac{Nx}{2}$ for some constant $c$. For a little perspective, I am going to ...
0
votes
0answers
52 views

Derivatives of hyperbolic functions and Osborne's rule.

I am slightly confused when it comes to Osborne's rule when you take derivatives of hyperbolic functions. For example. The derivative of cotx is -cosec^2x, so there is a product of sines. So should ...
0
votes
0answers
21 views

How to find the Laplace Transform of two (independent) functions multiplied together?

How does one find the laplace transform for an equation consisting of two trig functions multiplied together, when it is not possible to use any trig identities? For example, take a function say; ...
0
votes
0answers
34 views

Integral of trig fraction using substitution

I'm getting to grips with the process of integration by substitution, and would like to ask for feedback on my calculation: $$\int{\frac{\cos{x}}{\sqrt{1+2\sin{x}}}}\,\,dx$$ Let ...
0
votes
0answers
28 views

Manipulating multivariate trigonometric functions

I've manipulated a few trig identities but nothing seems to help me in showing that these two equations are equal. I'm pretty sure I haven't come across anything like this before, how do I ...
0
votes
0answers
25 views

$\int_0^\pi \cos{mx}\cos{nx}\,\mathrm{d}x$, with $m$ and $n$ integers

I can't figure out this integral at all. Integrating gave the following \begin{equation} \frac{1}{2}[\frac{\sin((m-n)x)}{m-n}+\frac{\sin((m+n)x)}{m+n}], \end{equation} but when I evaluate it from ...
0
votes
0answers
41 views

Find reflected angle off an arc

Note: Sorry if this question is elementary. I am trying to find the reflected angle when a ball hits a 10 degree arc. I know I have to use trigonometry in some way, but I am having trouble grasping ...
0
votes
0answers
94 views

Squeeze theorem and $\frac{\sin x}{x}$

I've been going over old calculus books to refresh my memory and have mainly been focusing on proofs. One of the things I found interesting was the squeeze theorem, even though since basic calculus i ...
0
votes
0answers
10 views

trigonometry - find coordinates of inner triangle after rotation

here is my situation: I have a rectangle I'm rotating 30 degrees counterclockwise, how could I use trig to get the 3 vertices (corners) and lengths of the purple triangle sides and hypotenuse ...
0
votes
0answers
36 views

Values of $\arctan(x)$ by hand

How can I solve arctan problems by hand? Is this a matter of hoping for good forms and memorizing a long list of them? My question had as part of it: $$z=1-\sqrt3i$$ and I can immediately see that ...
0
votes
0answers
45 views

Why is the argument of complex number determined up to integer multiple of $2 \pi$?

I have just started learning about complex number and came across to this argument of complex number Let's say we have a complex number $z$. Then the argument of $z$ can be represented by this: $arg ...
0
votes
0answers
35 views

How can you quickly ease a sine wave's amplitude?

I'm currently drawing a sine wave using the following function in java: Math.sin(x)*currentAmplitude The problem I'm experiencing is that, although this works ...
0
votes
0answers
43 views

How can I derive Polarization Operator algebraically

Can anyone describe for me the algebraic steps needed to create what Prof. Leonard Susskind calls, in one of his early Quantum Mechanics courses, the "Polarization Operator Matrix"? It is a 2 by 2 ...
0
votes
0answers
33 views

How to calculate Arc Cosine, without a unit circle.

How can I calculate the $\arccos(Y)$, neither using the trig functions on a calculator, nor using a unit circle? I would be satisfied if I got $\arcsin(Y)$ or $\arctan(Y)$ instead, but I would prefer ...