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

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How does one define appropriate branch cuts for arcsin(z) in the complex plane?

In learning about complex numbers, I have come across the following: http://upload.wikimedia.org/wikipedia/commons/b/be/Complex_arcsin.jpg Clearly, arcsin is multi-valued because it is a function of ...
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28 views

is there an existing formula in finding the area of a rhombus wherein only the side is given?

is there an existing formula in finding the area of a rhombus wherein only the side is given? No measure of angles, no lengths of diagonals , height, etc. is given.
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43 views

$Sin(a) Sin(b) == A (Sin(a) + K Sin(b))$

When $b$ is close to $\pi/2$, can we find an approximation like $$M \sin(a) \sin(b) = A (\sin(a) + K \sin(b))$$ or $$M \sin(a) \sin(F*b) = A (\sin(a) + K \sin(b))$$ or $$M \sin(F*a) \sin(b) = A ...
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why does $ \sqrt{1 - \cos^2\theta} $ = $ \sin\theta $

The question I have in the title is my question. Why does this simplify to sin? why does $ \sqrt{1 - \cos^2\theta} $ = $ \sin\theta $
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Geometry Problem relating similarity.

Given a triangle $ABC$ and $D$ be a point on side $AC$ such that $AB=DC$, angle $BAC=60-2x$, angle $DBC=5x$ and angle $BCA=3x$ prove that $x=10$. Source: 150 Nice Geometry Problems - Amir ...
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Construction of the equation from a given graph

The above diagram shows a sine-like graph is plotted in the range $0° \le x \le 360°$. It passes through 5 distinct points, namely A(0°, 0), B(90°, 2), C(180°, 0), D(270°, -2) and E(360°, 0). In ...
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Latitude and longitude of the destination of an airplane, given its speed and direction of travel

Problem A plane leaves an airport X, $20.6$ degree east and $36.8$ degree north, and flies due south along the same longitude for 8hrs at the rate of 1000km/h to another airport Y, $20.6$ degree east ...
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122 views

Why is Wolfram Alpha wrong?

I calculated $$\tan 75^o - [\cos 13^o\cdot \cot 23^o \cdot \tan 31^o \cdot \tan 35^o\cdot \tan41^o]$$ and I got a nonzero answer: ...
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Rotation of an object's acceleration

I want to track things that can rotate using acceleration. The visual involves overlaying two graphs rotated at different angles. This is needed because the accelerometer also rotates with the ...
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31 views

Recognize a shape with a set of Data points

So I have a number of points on graph. For Ex: (1,1) (2,5) ......... and so on. And I want to recognize which shape is it closest to from circle, triangle and rectangle. -By closest I mean ...
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69 views

Is there a 4 pointed star that is regular?

I am studying about the area of a 4 pointed star, I wonder if there is really a 4 pointed star that is regular? what could be the characteristics of a regular 4 pointed star? that is how i ...
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20 views

Trig Question Lemma Application

A trig lemma states that if $a^2 + b^2 = 1$, there exists such an angle that a = cos theta, b = sin theta. This lemma is the converse of a = cos x, b = sin x. I am then given an application ...
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17 views

Simultaneously solving trigonometric equations

Let $N\in\mathbb N$. Given $\theta_1,\ldots, \theta_N\in [0,2\pi)$ I would like to prove that there exist $\rho\in\mathbb R_+$ and $\varphi\in[0,2\pi)$ such that $$ f_\ell(\rho,\varphi):=\theta_\ell ...
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20 views

simplify and find domain for triginomic function

I am just doing some review and a question requires me to simplify and find the domain of this function, $\sin(2)\sin(2x)$ how do I find the domain?
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20 views

Bounds on sum of sines/angles.

I have the following equalities: $$ \sin(\theta) + b_x = sin(\theta_a) \\ \cos(\phi) + b_y = cos(\phi_a) $$ My goal is to find upper bounds for the following: $|\theta - \theta_a|$, $|\theta + ...
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23 views

when you draw 1 altitude/ perpendicular bisector of an equilateral triangle, what can you form?

when you draw 1 altitude/ perpendicular bisector of an equilateral triangle, what can you form such that when you draw 4 equilateral triangles the foot of the perpendicular of the equilateral ...
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23 views

Can a complex number have two arguments

Now, the reason why I wrote two $\theta$s is because my answer is the answer we get from $\theta$2 and the answer in the book is given the value of $\theta$1. So, I was just wondering whether both ...
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38 views

period of cubic trigonometric functions

Can anybody explain how you would find the period of cubic trigonometric function. so I need to find the period of $f(x)=\sin^2\left(\frac{x}{3}\right)$. So I have began the question by finding the ...
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23 views

solving 3D trigonometry

A 7m tall flag pole is placed exactly 5m in front of a north facing vertical wall. When the sun is north-west, the shadow of the pole just touches a vertical wall. Calculate the angle of elevation of ...
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23 views

How can this equation be simplified?

Can the equation $X=\log(f(t,d)+1)\times \sin(\frac{1}{1+\log(f(t,d)+1)})$ be simplified? The repeated term $\log(f(t,d)+1)$ suggests to me that it should be refactored but I can't see how.
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Is my proof of trigonometric equality correct?

I had a solved example in my book whose proof actually turned out to be different from what I did. I was just wondering whether whatever I have done is correct or I've missed something: Thanks, and ...
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30 views

Get Vector From Angle In $3D$ Space

I have a camera angle in $x,y,z$ with values between $0$ and $360$, I'm trying to compute this into an 'aim vector' which would have values between $0,0,0$ and $1,1,1$ depending on what the angles ...
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46 views

Calculating rotated relative positions on 2D plane

For a game project, I need to calculate positions of items on a 2D plane relative to the camera. Camera can be rotated, and it's coordinates refer to it's center. In the attached images, ...
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48 views

$\frac{\pi }{2}-\tan^{-1}\left(x\right)$ = $\tan^{-1}\left(\frac{1}{x}\right)$?

It's said that $$\frac{\pi }{2}-\tan^{-1}\left(x\right)=\tan^{-1}\left(\frac{1}{x}\right)\tag{1}$$ Well what about this. Lets say $$\frac{\pi }{2}-\tan^{-1}x=\frac{\left(\pi ...
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27 views

General solution of $\sin x$ and $\tan x$ when equal to $-1$.

Why don't we write the general solution of $\sin\left(x\right)=-1$ as $x=2n\pi +\left(-\frac{\pi }{2}\right)$ but rather $x=2n\pi +\frac{3\pi }{2}$. And if this is correct why do we write the ...
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60 views

How prove $\tan1^{\circ}+\tan7^{\circ}+…+\tan175^{\circ}=-30\sqrt3$?

How prove that $\tan1^{\circ}+\tan7^{\circ}+...+\tan175^{\circ}=-30\sqrt3$? I noticed that $1^{\circ},7^{\circ},...,175^{\circ}$ form an arithmetic.
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28 views

How to calculate the coordinate of a point which depends on other points on a plane with specific distances

I have $8$ points on a plane $(x_1,y_1)....(x_8,y_8)$ among these $8$ points I know the coordinates for $7$ points and I have to find the $8^{th}$ point. Each points has the difference between all ...
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42 views

Strategies to work with system of trigonometric inequality

I'm trying solve this problem using matlab, anybody know good strategies to work with system of trigonometric inequalities such as $ ...
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38 views

Formal Trigonometric Refrence

I'm Using a textbook for mathematic which is produced to learn for normal students. Here I'm giving the link of chapter of trigonometric functions of my textbook : ...
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31 views

Expand trigonometric expression

I am supposed to expand this expression $${\frac {\sin \left( x \right) b \left( 4\,b\cos \left( x \right) + \sqrt {16\,{b}^{2}+1}+5 \right) }{4\,b\cos \left( x \right) +\sqrt {16 \,{b}^{2}+1}+1}} $$ ...
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45 views

Trigonometry, find distance of arc movement

Imagine I have the setup as follows: I want to compute the height x in State 2, depending on how much the blue axis have moved. That is, the distance ...
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19 views

Steps involved in simplifying trigonometric identities.

I am trying to master the simplification of trigonometric identities. When I look at a problem, asking me to simplify a trigonometric expression, I am not really sure what to do - but I do sort of ...
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Worded trig question

From the top of a vertical cliff 125m high, the angle of depression to the top of a ship is 3.5°. If the ship is 1800m from the base of the cliff, determine the height of the ship above the water. I ...
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Finding Opening Angles (in an Algorithm)

I seem to be spending far too long on what I thought was an easy task. I have a set of polar points (I start with the XY coords). The angles are measured from the vertical, in a clockwise manner, as ...
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25 views

Looking for a method to solve simple trigonometric equations

Assume that $N$, $q$, $k_1$ and $k_2$ are integers such that $N>1$, $0\leq k_1<k_2<N$ and $q\geq 3$. Is there a method to solve the following trigonometric equation: $$ \sin\big(\frac{\pi ...
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Similar triangle, Quick question (Thick Lens Formula)

http://www.panohelp.com/thinlensformula.html On the right hand side, f is defined as focus of the lens, i understand why the image distance is (f + fm). However i have spent an afternoon and could ...
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Negative zero in atan2 calcs - what's the application?

I hope this is not considered a duplicate -- I asked a question about negative zero on StackOverflow and was told the question was better suited to a math-related SE site. To that end I'll try to ...
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70 views

Computing the coordinates of a point, offset from a rotated point.

Good day. I have a question which should be easy but I have not been able to figure it out. The coordinates of a point on a unit circle, given an angle, is $$\begin{align} x &= \cos(\alpha) \\ y ...
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Finding true bearings?

What is the true north bearing of NNE on 16 point cardinac compass? I just wanna know that is there any exact bearing or do we have to only give an approximate bearing?
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Find the relation the 'maps' 2D points to the corresponding 3D images.

I have this [on hold] question (#857264) re-phrased. Hope that the content is more meaningful now. The following is the picture modified from the original. The question is a rectangular piece of ...
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39 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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determine signal frequency and phase

let us consider following graph we should answer on the following question In the following figure, it is possible to measure both a positive and a negative value of $t_1$ and then calculate the ...
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Analytical Models for Hysteresis of Complicated Systems

I’ve been working with a system that exhibits hysteresis and I’ve found that the more common models do not work for me. I am wondering if anyone is aware of other models that might be out there for ...
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51 views

Trigonometry - proving a rule

I was given that $\sin a + \sin b + \sin c \cdots$ is equal to: (where $a,b,c$ are in arithmetic progression) $$\frac{\sin\frac{a + c}{2}\sin\frac{nb}{2}}{\sin{b/2}}$$ Here $a$ is the first term of ...
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Vector Magnitude during rotation

Probably something I should now already but this is confusing me no end! Lets say we have a force which is directed at 69 degrees inclination (from the X axis) with a magnitude of 500, shown below: ...
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Direct to indirect angle

I have a system which it computes angle in direct way and an other system in indirect. What is the formula to convert angles from one to other? Thx
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51 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) = ...
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27 views

Help in finding a book

That is my problem: i have this series: $\sum_{k=0}^{\infty} \psi_{k}(h)\cos(k\theta)$. I need to see to what it converges assuming something on the functions $\psi_{k}(h)$. There is a book or a site ...
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36 views

Relation btwn hyperbolic numbers and hyperbolic functions

Is there any relation between the hyperbolic (split-complex) numbers and hyperbolic trig functions? Or are they just named similarly by accident?
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Rotating a triangle in different coordinate systems.

My android application uses openGL. OpenGL coordinate system has the origin in the middle and goes from -1 to 1. When I am rotating an equilateral triangle in the openGL coordinates, the triangle ...