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

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1answer
171 views

What conic curve is the graph of y=sin(x) from 0 to pi?

Certainly is not a circle; it looks like an ellipse but I don't think it is. Thanks
6
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3answers
816 views

Simultaneous equations, trig functions and the existence of solutions

Came across this conundrum while going over the proof that $$A \cdot \sin(bx) + B \cdot \cos(bx) = C \cdot \sin(bx + k)$$ for some numbers $C$ and $k$. ($A$, $B$ and $b$ are known.) The usual method ...
2
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2answers
292 views

Solving short trigo equation with sine - need some help!

From the relation $M=E-\epsilon\cdot\sin(E)$, I need to find the value of E, knowing the two other parameters. How should I go about this? This is part of a computation which will be done quite a ...
14
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4answers
951 views

Finding $\int_0^{\pi/2} \sin x\,dx$

I'm interested in why $$\int_0^{\pi/2} \sin x\,dx = 1.$$ I know how to do the integral the conventional way but am more interested in what makes radians special for this problem. If we instead compute ...
2
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2answers
613 views

Trig Question - $\arcsin(\sqrt{2}/2)$ and arc trig functions in general

I know $\arcsin(\sqrt{2}/2)$ is equal to $\pi/4$. However I don't understand why, I've done some searching on google about arc trig functions and I haven't found any webpages that explain it very ...
2
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2answers
253 views

What is the simplification of $\sin^2 x/(1+ \sin^2 x +\sin^4 x +\sin^6 x + \cdots)$?

What is the simplification of $\sin^2 x/(1+ \sin^2 x +\sin^4 x +\sin^6 x + \cdots)$?
9
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2answers
547 views

New size of a rotated-then-cropped rectangle

Imagine a rectangle (x1 by y1) always has to be drawn with horizontal and vertical lines (so it can't have lines at 45 degrees). If the rectangle is rotated by angle θ, it needs to have a rectangle ...
1
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2answers
207 views

Simplifying a Trigonometric Expression

I have to prove that: $$x \sec x - \ln |\sec x + \tan x| + C$$ is the indefinite integral of: $$x \sec x \tan x $$ by taking the derivative. I've got far enough to get: $$x\sec x\tan x + \sec x ...
3
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1answer
243 views

Graph for $f(x)=\sin x\cos x$

Okay, so in my math homework I'm supposed to draw a graph of the following function: $$f(x)=\sin x \cos x.$$ I have the solution in the textbook, but I just can't figure out how they got to that. So, ...
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5answers
2k views

Solve $\cos(\theta) + \sin(\theta) = x$ for known $x$, unknown $\theta$?

After looking at the list of trigonometric identities, I can't seem to find a way to solve this. Is it solvable? $$\cos(\theta) + \sin(\theta) = x.$$ What if I added another equation to the problem: ...
2
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1answer
358 views

How to solve algebraically the equation $x = \frac{1}{2}\cos\left(\frac 2 3 \sin\left(\frac 3 4 x\right)\right) + 1$

How to solve this trigonometric equation $x = \frac 1 2 \cos\left(\frac 2 3 \sin\left(\frac 3 4 x\right)\right) + 1$ ? The iterative solution seems to be 1.417. Can anybody suggest an algebraic ...
2
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3answers
500 views

Why are there two possible triangles when given SAS?

I gave my trigonometry students the following example: Solve $\triangle ABC\ $ , where AC=0.923, AB=.387, and $\measuredangle A\ = 43.33^\circ\ $. First I found BC using the law of cosines, then I ...
3
votes
3answers
290 views

Trigonometric equality

I would like to know, how do you simplify this: $$\cos x\sin(x+y) + \sin x\cos(x+y)$$ to this: $$\sin(2x+y).$$ Wolfram alpha says so, but how does human being do so? :)
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2answers
115 views

Radius of a hypercube at a given angle

For a ray from the origin with a given angle in $R^n$, I am trying to find the radius at which that ray intersects the frontier of the unit n-cube. In two dimensions, the picture is this: Given ...
8
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3answers
1k views

Name of this identity? $\int e^{\alpha x}\cos(\beta x) \space dx = \frac{e^{\alpha x} (\alpha \cos(\beta x)+\beta \sin(\beta x))}{\alpha^2+\beta^2}$

Again: $$\int e^{\alpha x}\cos(\beta x) \space dx = \frac{e^{\alpha x} (\alpha \cos(\beta x)+\beta \sin(\beta x))}{\alpha^2+\beta^2}$$ Also the one for $\sin$: $$\int e^{\alpha x}\sin(\beta x) ...
2
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2answers
156 views

Trigonometry Expression

Is $(\sin \phi)^2$ is equal to $\sin^2\phi$? Can any one tell what is the ans for the below expression $\sin^260$ + $\cos^260$ + $\tan^245$ + $\sec^260$ - $\csc^260$
3
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2answers
139 views

Help with using some trig identities

Need some help with the steps in converting the derivatives of the following functions. derivative of $\cos(\tan(x))$ to $\frac{-\sin(\tan (x))}{\cos^2(x)}$ I can get $-\sec^2(x) \cdot ...
6
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5answers
1k views

If $\sin x + \cos x = \frac{\sqrt{3} + 1}{2}$ then $\tan x + \cot x=?$

Hello :) I hit a problem. If $\sin x + \cos x = \frac{\sqrt{3} + 1}{2}$, then how much is $\tan x + \cot x$?
2
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2answers
636 views

How can I solve for a single variable which occurs in multiple trigonometric functions in an equation?

This is a pretty dumb question, but it's been a while since I had to do math like this and it's escaping me at the moment (actually, I'm not sure I ever knew how to do this. I remember the basic ...
2
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4answers
780 views

What is the limit as $x\to\infty$ of $\cos x$?

What is the limit as $x\to\infty$ of $\cos x$? Thanks in advance.
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5answers
641 views

Simpler solution to this geometry/trig problem?

i had a geometry/trignometry problem come up at work today, and i've been out of school too long: i've lost my tools. i'm starting with a rectangle of known width (...
3
votes
1answer
113 views

Proving equation at zero?

I have an equation $$x = \csc(\theta) - \cot(\theta).$$ As $\theta$ approaches zero, $x$ approaches zero. However, trying to solve the equation at zero yields an undefined result. How do I rewrite ...
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2answers
3k views

How can we sum up $\sin$ and $\cos$ series when the angles are in arithmetic progression?

How can we sum up $\sin$ and $\cos$ series when the angles are in A.P (arithmetic progression) ?For example here is the sum of $\cos$ series: $$\large \sum_{k=0}^{n-1}\cos (a+k \cdot d) =\frac{\sin(n ...
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3answers
360 views

basics of Trigonometry

I have learned trigonometry, in school but never understood clearly what it is..just mugged up formula's and theorems to get clear the exams. But now i want to know what exactly, is trigonometry from ...
2
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3answers
156 views

How does teacher get first step?

Below are the steps the teacher took to solve: $y = \sqrt{3}\sin x + \cos x$ find min and max on $[0, 2\pi)$ Step 1: = $2\sin(x + \pi/6))$ How does the teacher get this first step? Note: No ...
2
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2answers
7k views

min and max of trig function

I'm trying to help a friend of mine solve this problem. It's been like 10 years since I took calculus please help: Find min/max values of $y = \sin x + \cos x$ on $[0, 2\pi)$ Thanks. I've got this ...
5
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1answer
628 views

How to “shrink” a triangle

Given any triangle (vertices are known) and a distance X, how can I compute the triangle that is shrunk by X from the original? By shrink, I mean edges of the shrunk triangle are exactly X away from ...
2
votes
1answer
813 views

What does the little d and d^2 mean in equations?

I'm reading a text on ray tracing. There is this section about radiometric quantities where radiance is defined as $L = \frac{d^2\Phi}{dA cos\Theta d\omega}$ $\Phi$ is the radiant flux $\Theta$ is ...
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2answers
311 views

Angle for pointing at a certain point in 2d space

Recently, I have been programming a simple game. Very simple: There is a tank, and the cannon will aim at whatever position the mouse is at. Now lets talk about the cannon graphic. The cannon graphic ...
3
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3answers
198 views

Apparent inconsistency between integral table and integration using trigonometric identity

According to my textbook: $$\int_{-L}^{L} \cos\frac{n \pi x}{L} \cos\frac{m \pi x}{L} dx = \begin{cases} 0 & \mbox{if } n \neq m \\ L & \mbox{if } n = m \neq 0 \\ ...
2
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2answers
243 views

Is $\sin\frac{1}{x} \lt \frac{1}{x},\ \forall x\geq 1$?

Is $\sin\frac{1}{x} \lt \frac{1}{x},\ \forall x\geq 1$? I tried "copying" the proof of $\ln x \lt x, \forall x\geq 1$ but it didn't quite work. Here's what I did: Let ...
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1answer
395 views

Is it possible to calculate an angle of movement from the horizontal from accelerometer and magnetometer data?

I have a home made device (think baseball) with an accelerometer and a magnetometer embedded within it and would like to capture some details of an attempted 'throw' of the device. All I need is the ...
1
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1answer
234 views

How do you generate mathematical formulas programmatically using a server side language [closed]

We would like to generate simple mathematical formulas on the fly (e.g. $\sin^2 \theta$). The above function seems to be a MathJaX representation. Most of the solutions depend on writing mathematical ...
2
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2answers
4k views

Find Coordinates of Touching Point of a Tangent on a Circle

I have a point 'a' with known coordinates, from which I have drawn a tangent to a circle with centre 'c' which is also known. What is the best way of finding the coordinates of point 'b', the touching ...
6
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1answer
790 views

Sine values being rational

Can $$\sin r\pi $$ be rational if $r$ is irrational? Either a direct or existence proof is fine.
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3answers
2k views

How can I find the derivative of $y = \sin(\arctan x) + \tan(\arcsin x)$?

My question is, how can I solve the following derivative question? $$y = \sin(\arctan x) + \tan(\arcsin x)$$ Thanks in advance
4
votes
4answers
422 views

How can I find $ \int{(1 + \cos x)^3\mathrm dx} $?

My question is ; How can I solve the following integral question? $$\int{(1 + \cos x)^3\mathrm dx}$$ Thanks in advance,
1
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0answers
608 views

How do I calculate the cartesian coordinates of stars

Given the Right ascension in h m s, Declination in deg ' " and the Trigonometric parallax How can I get the cartesian (x,y,z) coordinates of a star? I'm guessing I need 3 separate formulas to get each ...
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1answer
744 views

Find the Angle ( as Measured in Counter Clock Wise Direction) Between Two Edges

This is a similar question to this one, but slightly different. The question is given two edges ($e_1$ and $e_2$, with the vertex coordinates known), how to find the angles from $e_1$ to $e_2$, with ...
2
votes
2answers
147 views

Find the Outgoing Edge with the Smallest Angles, Given one Incident Edges and Multiple Outgoing Edges

I have one incident edges and multiple outgoing Edges, for which I want to pick an outgoing edge such that the angles between the outgoing edge and the incoming edge is the smallest of all. We know ...
1
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3answers
341 views

How do I find the area or the volume (or a formula) for a region that is rectangular but has a cone slope to a drain?

This is a quick (not to scale) drawing of what I mean: the floor gradually slopes from the wall to the drain at about 7/16( 0.4375) inch per foot from the short sides of the wall (the 7 ft from wall ...
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7answers
869 views

Limit, solution in unusual way

I have a problem with solution of this limit: $$\lim_{x\to 0}{\frac{\tan{x}-x}{x^2}}$$ Of course, it's a very easy to solve, using (twice) L'Hôpital's rule, but I need to find out, how to do this ...
2
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4answers
409 views

How can I find $\int\tan\;x\;\cos\;2x\;\mathrm dx$?

My question is ; How can I solve the following integral question? $$\int\tan\;x\;\cos\;2x\;\mathrm dx$$ Thanks in advance,
2
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1answer
314 views

recursively defined trigonometric sequence and Cesàro means

So, we have a function $$f(x) = \frac{3\sin(x)}{2 + \cos(x)} $$ and we fix a point $$ x_0 \in \left(0, \frac{2\pi}{3}\right] $$ and define a sequence by setting $$ x_{n+1} = f(x_n) $$ Now I need ...
0
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4answers
854 views

Finding X and Y coordinates from two angles

I have a triangle ABC in the x-y coordinate plane. Corners A and B lie on x-axis. Length of AB is known. Angles A and B are also known. Question: Find (x,y) coordinates of corner C.
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1answer
199 views

quaternion to angle

Alright, so this is how I am doing it: ...
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1answer
843 views

Help with calculating the angle to turn towards a target in a coordinatesystem

I know the following: my own position my own facing (the angle im turned) my targets position What i would like some help with is how i calculate the shortes way to turn and the angle to turn. If ...
2
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2answers
839 views

integral of $\arcsin(\sin(x))$

I'm having trouble with this integral $$\int\arcsin(\sin x)\,\mathrm dx$$ The problem is with the intervals of definition for each function :/ if someone could dumb it down for me. ...
5
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3answers
1k views

How to determine arc measures from angles between secant and tangents (without trigonometry)

Given a circle, a point $H$ outside the circle, segments $\overline{HE}$ and $\overline{HT}$ tangent to the circle at $E$ and $T$, respectively, and points $I$ and $G$ on the circle such that $I$, ...
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1answer
152 views

Getting the % that a point is on a line

Alright, so I got two points in 3d space, so they have a x,y, and z. Now if the line's y - which I get like so: ...