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

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Law of Sine Problem

I know the law of Sine. SinA/a=SinB/b=SinC/c I think I'm missing something here... I am given ∠A=68.41°,∠B=54.23° and a=12.75ft. I found b with no trouble which is 11.119ft. I used SinA/a=SinB/b... ...
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1answer
19 views

How to rotate a line in 3d space? [on hold]

I am trying to figure out direction vectors of the arrowheads of an arrow. Basically I'm given a normalized direction vector ...
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2answers
9 views

How to find opposite and adjacent lengths of a right triangle given the hypotenuse and angle?

I'm writing a few functions for a JavaScript game engine. Is it possible to calculate the length of the legs of a right triangle given ONLY the length of the hypotenuse and an angle?
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1answer
20 views

Trigonometry - Conceptual Questions [on hold]

If anyone could help me solve these questions and provide steps, I would really appreciate it! Thanks in advance!
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0answers
29 views

Trigonometry - Proofs and Derivations [on hold]

Can someone help me solve this? I need to see steps so that I can work out other homework questions just like this. I would really appreciate any help! Thanks in advance!
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1answer
17 views

Finding the value of trigonometric functions

This is probably one of the easiest concepts but I do not get it, so I am going to give the two problems that are giving me the most trouble on my very long worksheet I have to do, maybe you guys can ...
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1answer
26 views

Integrating an equation with both cos and tan

$$\int2\cos^5x\cdot\tan^6x\cdot dx$$ $$2\int\cos^5x\cdot\frac{\sin^6x}{\cos^6x}\cdot dx$$ $$2\int \frac{\sin^6x}{\cos{x}} dx$$ $$2\int\cos^{-2}x\cdot \sin^6x\cdot \cos{x}\cdot dx$$ ...
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3answers
44 views

I have problem with Trigonometry

Tomorrow I have a test and there is one exercise in my textbook that isn't explained. Here is the exercise. ...
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0answers
24 views

Real world tangent functions

I am a high school math teacher and one of my students asked me for examples of real world tangent functions. Not using tangent to find a side length but a relationship that can be represented by a ...
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1answer
34 views

When to use what inverse trig?

When do I use $\arcsin$ and when do I need to include all of the outcomes? My gut feeling is if you have an equation like $\sin(x)=0$, then $x=0,\pi,2\pi...$ whilst if you are using it in integration ...
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1answer
38 views

When is $ 4 ab \sin^2 θ = (a+b)^2 $ ?

I know that by trial and error it is only possible when $ a=b $, but what is the actual solution process?
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0answers
25 views

Weierstrass function

I got stuck on this exercise from Prof. Tao's real analysis notes. Let $f:\mathbb{R}\rightarrow \mathbb{R}$ be the function $$f:= \sum_{n=1}^\infty 4^{-n} \sin(8^n\pi x)$$ Show that for every 8-dyadic ...
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3answers
42 views

Problem with trigonometric equation

I am having trouble solving this equation $$4\cdot \sin \theta + 2 \cdot \sin 2\theta =5$$ Thank you for your help.
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2answers
23 views

Trig Identity Proofs

I'm having a really hard time understanding how to do these. The directions are to verify that each of the following is an identity: $$\dfrac{\csc x}{\cot x+\tan x}=\cos x$$ I have to get the left ...
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2answers
19 views

Express the following in terms of $q$.

Given that $\cos{160^{\circ}} = -q$, express $\cos70^{\circ}$ in terms of $q$. No example in the book, don't know how to do it?? I need a complete explanation.
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1answer
29 views

Can I find this trigonometric expression without a calculator?

I know that $\sin A= 0.75$ will give me the answer of $A= 48.6^\circ$ or $\ 131^\circ$. Is there a way to find what $A$ equals manually. Thank you.
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3answers
28 views

Problem with this Trigonometric Equation

I am having trouble figuring out how to solve such an equation can anyone please tell me the steps to solve it as I have been solving a lot of trigonometric equations but I am stuck in this one: ...
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1answer
24 views

Trigonometric problem

I am having trouble solving simple trigonometric equations without a calculator which I am required to be doing in my course since I cant get to understand how to get for example sin x=-1/2 I know sin ...
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1answer
38 views

Sum of fractions of squared sines

I'm trying to prove the following approximate identity for $p$ integer: $$ \sum_{l=1}^m\frac{\sin^2\left(\frac{\pi l}{p}\right)}{\sin^2\left(\frac{\pi l}{mp}\right)}\sim \frac{m^2(p-1)}{2}+O(m) $$ ...
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1answer
16 views

Simple algebraic question mixed up

I know it is very simple but do not know why I am mixed up in it $(.5)(r^2)\cfrac{20-2r}r$ how is this equal to $10r-r^2$ Sorry if it is too easy, thanks for the help.
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1answer
22 views

Trigonometric equation problem.

Simply and shortly how do I show that this $33 = 33 + 5 \cos(720\cdot t)$ is equal to this $720 \cdot t = 90.$ Thank you for your help.
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0answers
12 views

Drawing Camera Image Area on Camera View

I have two camera images. The first image is a pulled back "overview image". In the second image I've zoomed the camera into a position on the original image. I want to draw on the first image a ...
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0answers
40 views

How find the range value $a^2+b^2$ if $\cos{(a\sin{x})}=\sin{(b\cos{x})}$ have no solution

if the equation $$\cos{(a\sin{x})}=\sin{(b\cos{x})}$$ have no zero solution,then $a^2+b^2$ range of value $A:[0,\dfrac{\pi}{4})$,$B: [0,\dfrac{\pi^2}{2})$,$C: ...
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4answers
22 views

Minimum value Of trigonometry expression

FIND THE MIN VALUE OF 4 cosec^2 x + 9 sin^2 x ? Please explain by both calculus and non-calculus methods ?
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2answers
15 views

Minimum value of trigonometric functions

What will be the min value of cosec x -sinx .Differentiating and setting it to zero is fetching me nothing meaningful. Plz explain how to go for such cosec and sec functions ?
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0answers
32 views

Finding the inverse of trig functions

I'm supposed to find the inverse of $$f(x) = \cos(x)+x$$ I usually just substitute $x$ for $y$ and then re-arrange. What do I do in this scenario?
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6answers
96 views

explicit expression sought

Consider the equation $$ \cos^2\phi + \alpha\sin\phi\cos\phi-\beta=0\;, $$ where $\alpha,\beta\in\mathbb{R}$. I need to find an explicit expression for $\phi$. I have tried completing the square, but ...
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1answer
37 views

Finite-case symmetry leads to infinite-case asymmetry

Formulas for sines or cosines of sums superficially appear to have a certain symmetry, specifically it looks as if sine and cosine play something like symmetrical roles: $$ \begin{align} & ...
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2answers
29 views

Complex Numbers and Hyperbolic Functions

How would you evaluate: $\mathfrak{R}\left[(1+i)\sin\left(\dfrac{(2+i)\pi}{4}\right)\right]$? I know that $\cos x = \dfrac{e^{ix}+e^{-ix}}{2}$ and $\sin x = \dfrac{e^{ix}-e^{-ix}}{2i}$. I have also ...
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1answer
34 views

Inverse trig and trigh in integration?

I have just done part (iii) of this question and can get the right answer but am a bit confused why do we take arcosh i.e. just the principle value of cosh and not the other value. I presume this is ...
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1answer
39 views

How to solve this trignometric equation?

I was given a circle with a radius of 3 and in it was a rectangle and an angle theta extending from the x axis to up with coordinates of (3 cos theta,3 sin theta) and the question asks me to show that ...
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2answers
39 views

Ordinary differential equation $y'(t)=\sin(f(t,y))$

One whose solution never makes me happy is the following: $$y'(t)=\sin(y+t)\text{.}$$ I would start by substituting $z(t)=y(t)+t$ to get an ODE in $z(t)$, but then I'm not sure about how to substitute ...
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1answer
39 views

How do I multiple these matrices together?

As a personal brain exercise, I've recently been trying to work out the math involved with rotating vertices around an arbitrary axis in 3D space. To do so, I've been relying very heavily on the ...
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1answer
16 views

Compound Angles

I'm working on compound angles formula problems, when i encountered this problem, sin(5pi/9) cos(7pi/18) I know how to use the formula, but I'm not sure how to break up these two angles into ...
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2answers
54 views

Is 1 rad important?

Of course radians generally come in ratios of π. So is 1 rad important/useful/special? Or, for that matter, is any integer radian measure important? Besides being approximately 57°, I can't seem to ...
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1answer
25 views

How do I simplify this difference of angles expression using conjugates?

I'm trying to fill in the gaps in my knowledge of simplifying rational expressions using conjugates, but this one stumps me. Given $\tan(\frac{\pi}{4}-\frac{\pi}{6})$, I can work the formula down to: ...
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2answers
27 views

Show this function can be defined as the limit function

Let f: $ \mathbb{R} \rightarrow \mathbb{R} $ be defined by f(x) = 1 for x $\in \mathbb{Q} $, f(x) = 0 otherwise. We can see f is not regulated. Show that f may be obtained as a limit function: f(x) = ...
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2answers
16 views

Find extrema on the interval

Problem Find the extrema of the function $$f(x) = cos^2(x)$$ on the interval $ [-4,4]$ I can differentiate and get $$f'(x) = -2 \sin(x) \cos(x)$$ And set that to zero, but I'm pretty sure that's ...
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2answers
21 views

Multiply segment

Suppose that I have the segment between the points (2, 2) and (3, 4). Empirically, drawing on a piece of paper, I can say that "doubling" the segment leads me to the segment (2, 2), (4, 6) and making ...
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4answers
54 views

How to solve trigonometric equations of the form $\tan(x)=m$ where $m$ is a real number?

How to solve trigonometric equations of the form $\tan(x)=m$ where $m$ is a number? I know how to solve $\sin(x)=m$ where $m$ is a real number and $\cos(x)=m$ where $m$ is a real number but I don't ...
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0answers
31 views

Given a non-negative integer $m$ and a positive integer $n$, calculate $\lfloor \frac{m}{n} \rfloor$

Here is the problem: I have a non-negative integer $m$ and a positive integer $n$ I would like to calculate $\lfloor \frac{m}{n} \rfloor$, $\lceil \frac{m}{n} \rceil$ and $m \bmod n$ But I want to ...
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0answers
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contradiction inverse function derivative [on hold]

in the cylindrical coordinate, when $\{x=r cosθ, y=r sinθ, r=\sqrt{(x^2+y^2 )}\}$ for example the partial derivative $\frac{∂r}{∂y}=\frac{1}{2} (x^2+y^2)^{(\frac{1}{2}-1)} \cdot 2y= ...
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2answers
85 views

Show that $\sin 10^\circ$ is irrational

So, this is the problem I am working on. Show that $\sin 10^\circ$ is irrational. The solution to the problem is $$1/2 = \sin 30^\circ = 3 \sin 10^\circ - 4\sin^3 10^\circ .$$ Let $$x = 2\sin ...
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1answer
43 views

How do I prove this Triginomerty equasion?

I got this in a math preparation course I'm taking for college. Can you please help me proving this? $$\frac{\sin2a\cos a-\cos3a\sin a}{2\sin a}=\cos a$$ Thanks!
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3answers
179 views

How prove this $\cos{x}+\cos{y}+\cos{z}=1$

Question: let $x,y,z\in R$ and such $x+y+z=\pi$,and such $$\tan{\dfrac{y+z-x}{4}}+\tan{\dfrac{x+z-y}{4}}+\tan{\dfrac{x+y-z}{4}}=1$$ show that $$\cos{x}+\cos{y}+\cos{z}=1$$ My idea: let ...
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0answers
28 views

Phase vocoder equation

I know I can adjust the frequency of a waveform using a modified version of the sine wave equation amplitude*cos(2*pi*frequency*time+phase) this will allow me to adjust the frequency of a signal. ...
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2answers
31 views

area of ​​a quadrilateral

Get the area of ​​a quadrilateral? $‎\angle ‎A‎‎‎_{1}‎+‎\angle ‎C‎_{3}‎=30‎^{‎\circ‎}‎‎‎‎‎$‎ $\angle ‎A‎‎‎_{2}‎+‎\angle ‎C‎_{4}‎=90‎^{‎\circ‎}‎‎‎$ $CD=9, DA=5, BC=8 , AB=4$
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2answers
16 views

Condition of periodic function for |sin πx|

Period of |sin πx| = 1 Wolfram alpha : So why this condition for Periodic function is not true? f(x) = f(x + T) Wolfram alpha :
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1answer
20 views

Why do I get a domain error for the following computation using law of cosines

Following are two points. lat1, lon1 represent one point and lat2, lon2 represent another point. ...
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1answer
11 views

Obtaining consistent triangle surface normals.

I am given 3 points in a random order like so... calculateSurfaceNormal(point1, point2, point3); I have implemented the method by simply saying... ...