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

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-1
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1answer
33 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 ...
1
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2answers
25 views

Verify :$\cos^2x=\cot^2x-\frac{\cos^2x}{\tan^2x}$

$$\cos^2x=\cot^2x-\frac{\cos^2x}{\tan^2x}$$ How can I solve it?
0
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1answer
20 views

Simplifying Trig Identity

I have an equation I have been given to solve, I know how to start but I do not know what to do after I use the Trig Identities. Any help? Here is what I was given $$ \frac{\cos(A + B) + \cos(A - ...
2
votes
1answer
199 views

Goat tethered in a circular field

I need help on this question. I was thinking of counting the area of the whole circle and then subtracting it with the area that is not eaten by the goat. But I don't know how to find this particular ...
4
votes
2answers
73 views

Showing $\sin{\frac{\pi}{13}} \cdot \sin{\frac{2\pi}{13}} \cdot \sin{\frac{3\pi}{13}} \cdots \sin{\frac{6\pi}{13}} = \frac{\sqrt{13}}{64}$

I would like to show that $$ \sin{\frac{\pi}{13}} \cdot \sin{\frac{2\pi}{13}} \cdot \sin{\frac{3\pi}{13}} \cdots \sin{\frac{6\pi}{13}} = \frac{\sqrt{13}}{64} $$ I've been working on this for a few ...
0
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1answer
14 views

Sketch the graph for $0^\circ \leqslant x \leqslant 360^\circ$.

Sketch the graph $y= cos \frac{3}{4}x-2$ for $0^\circ \leqslant x \leqslant 360^\circ$. Please help me draw this. I found out that $y= cos \frac{3}{4}x-2$ has a period of ...
0
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1answer
13 views

Find the resulting speed and direction

A barge is pulled by two tugboats. The first tugboat is traveling at a speed of 15 knots with heading 130°, and the second tugboat is traveling at a speed of 16 knots with heading 190°. Find the ...
0
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1answer
18 views

From centroid and two vertexes to find the missing vertex of a triangle.

The centroid of triange $ABC$ is located at $P(14,14)$ with points $A(2,12)$ and $B(22,6)$ What are the coordinates of vertex $C$? Explain how you found the answer. I've gotten a question of the ...
0
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2answers
21 views

Solving for x on unit circle equation

I have been given the equation $$\cos^2{x} + 2\sin{x}=2.$$ I have factored it, and the only answer I got was $x=\frac{\pi}{2}$. Is this correct or is there more than one answer? The interval is $0 ...
0
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2answers
18 views

Inequality: $\tan(x) > 1$

So far, I've not come very... far. It ends up with me trying to solve it more intuitively than mathematically. I figured, first I'll find the place of equality, which is at $x = \arctan 1 = ...
0
votes
2answers
80 views

How does the unit circle work for trigonometric ratios of non-acute angles?

How does the unit circle work for trigonometric ratios of obtuse angles? I know that the x coordinate is $cos (\theta )$ and the y coordinate is $sin (\theta )$. But I understand these in context of ...
-1
votes
1answer
21 views

How to find coordinates of the center of circle containing a given arc [on hold]

Given: Coordinates for each end of circular arc, angle of arc, radius length. How do I find the coordinates of the center of the circle containing the arc?
1
vote
1answer
5 views

Finding (sin(A+B))^2 given roots of a quadratic equation.

If tan A and tan B are the roots of the equation x^2 -ax + b = 0, then the value of sin(A+B)^2 is? Options are: ((a^2)/((a^2)+(1-b)^2), (a^2)/(a^2+b^2), a^2/(b+a)^2, a^2/(b^2*(1-a)^2) The value ...
2
votes
4answers
394 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,
8
votes
7answers
790 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 ...
0
votes
2answers
13 views

“Which is equivalent for restricted x values to”

I've been checking my homework via Wolfram Alpha, and for several questions (example below) in this section (trigonometric integrals). I'd be correct up until the last step, in which Wolfram Alpha ...
3
votes
3answers
115 views

Proving $\csc (x) +\cot( x)=\frac{\sin (x)}{1-\cos(x)}$

I have this problem: Prove that $\csc (x) +\cot( x)=\dfrac{\sin (x)}{1-\cos(x)}$ From LHS I tried using $\sin^2x+\cos^2x = 1$ and ended up nowhere. I tried rearranging RHS but ended up with ...
2
votes
2answers
90 views

How do you find the height of a triangle given $3$ angles and the base side? Image given.

This question has me absolutely stumped. This is the image of the question, how can I work out $x$? I've been doing a variety of attempts but I just cant get it.
0
votes
1answer
54 views

Find the solutions of: $\sin x+\cos x=\sin^2 x+0.5\sin{2x}$

Find the solutions of: $\sin x+\cos x=\sin ^2 x+0.5\sin{(2x)}$ How can I find the solutions ?
0
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1answer
13 views

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
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!
2
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2answers
15 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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0answers
30 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!
1
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2answers
210 views

Formula to find the third point of triangle when two points and all sides are known?

I am writing a program in java. I looking for formula to determine the 3rd point in a triangle if the length of all sides and the coordinates of two points are known.
0
votes
1answer
19 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 ...
1
vote
1answer
29 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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4answers
2k views

Finding the perimeter for a triangle $ABC$ given a side, angle, and the area

Given a triangle $ABC$, $\angle C$ is $65$ degrees, side $C$ is 10. The area of the triangle is $20.$ What is the perimeter?
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3answers
50 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. ...
0
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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 ...
0
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1answer
21 views

Trigonometry for steradian angle

Polar coordinate system is very closely associated with trigonometry. For instance, given an angle in radian, we can find its corresponding 2-D cartesian coordinates using ...
0
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1answer
36 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
40 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?
1
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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.
1
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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 ...
16
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4answers
260 views

Prove: $\sin (\tan x) \geq {x}$

I bumped into this question: Question: Prove that for $x\in \Bigl[0,\dfrac {\pi}{4}\Bigr]$, $$\sin (\tan x) \geq {x}$$ This seems to be an innocent inequality but I am already exhausted trying ...
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3answers
159 views

Curve to fit points

I'm trying to find the equation that fits the following points: $1,0.0105; 2,0.181; 3,0.47; 4,0.755; 5,1.01; 6,1.22; 7,1.39; 8,1.54; 9,1.67; 10,1.79; 11,1.88; 12,1.96; 13,2.03; 14,2.10; 15,2.15; ...
0
votes
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 ...
0
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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.
3
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1answer
38 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} & ...
1
vote
4answers
105 views

Approximation to $\sqrt{\cos(\theta)}$?

I have this formula, (it is just the law of cosines angle formula): $$ d = \sqrt{a^2 + b^2 - 2ab \ cos(\theta)} $$ Here is my issue. I am wondering if there is a way to 'extract' the $cos$ term. My ...
2
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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.
0
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3answers
29 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: ...
0
votes
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 ...
2
votes
1answer
38 views

Sum of fractions of squared sines

I'm trying to prove the following approximate identity for $p$ integer: $$ \sum_{l=1}^m\frac{\sin^2\left(\frac{\pi l}{p}\right)}{\sin^2\left(\frac{\pi l}{mp}\right)}\sim \frac{m^2(p-1)}{2}+O(m) $$ ...
0
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1answer
17 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.
5
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11answers
960 views

How to solve $ \int_0^{\pi} \sin{2x}\sin{x} dx $?

How to solve $$\int_0^{\pi} \sin{2x}\sin{x} dx$$ Edit: Sorry! I should have described more. This is not a homework. Recently, Out of the blue I got interest in physics and started reading and solving ...
0
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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.
1
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2answers
70 views

Positivness of the sum of $\frac{\sin(2k-1)x}{2k-1}$.

For $n\in \mathbb{N}$, $x\in (0,\pi)$. Prove that : $$f_n(x)=\sum_{k=1}^n \frac{\sin [(2k-1)x]}{2k-1} \geq 0.$$ I've tried to do it by differentiation : I Calculate $f_n'(x)$ (sum of ...
0
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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... ...
0
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0answers
13 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 ...