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

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0
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2answers
31 views

Find the height of statue.

Standing on one side of a 10 meter wide straight road, a man finds that the angle of elevation of a statue located on the same side of the road is X. After crossing the road by the shortest possible ...
1
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2answers
47 views

A theoretic question about cosine general solution.

I have to find the extremas of: $f(x)=x-\tan({x\over 2})$ .$(\pi\le x\le\pi)$ Last result is $\cos({x\over 2})=\pm{1\over \sqrt{2}}$. I get that: ${x\over 2}=\pm{\pi\over 4}+2\pi k$ which derives: ...
-1
votes
1answer
21 views

Approximation for the Summation of Sequence of Powers of Sines Functions.

Let $z_1,z_2,...,z_m$ be real numbers such that $0<z_1,z_2,\ldots,z_m<\pi/2$, $z_1>z_2>...>z_m$ and $n$ an integer such that $n>0$. Prove that: ...
1
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1answer
21 views

why is the domain of $\sec^{-1} x$, $\mathbb{R}- (-1 ,1)$? why can't $x$ take a values like 0.2, 0.3, etc?

Why is the domain of $\sec^{-1} x$, $\mathbb{R}- (-1 ,1)$? why can't $x$ take a values like $0.2, 0.3$ or $0$?
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2answers
43 views

pls help to simpify [on hold]

pls help to simpify: $\sqrt{\frac{1+\cos x}{1-\cos x}}$
0
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3answers
58 views

Given $\frac{\sin(A - B)}{\sin(A+B)} = \frac57$, show $\tan A = 6 \tan B$

I can expand the sine using compound angle formula but then I can't continue to make it become a tangent.
1
vote
1answer
23 views

At how many points will $\lfloor(sin x + cos x )\rfloor$ be discontinuous in the interval [0,2$\pi$]

At how many points will $\lfloor(sin x + cos x )\rfloor$ be discontinuous in the interval [0,2$\pi$] ? How should the graph be ?
-3
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2answers
49 views

Need confirmation that the following problem is correct. [on hold]

I have to prove the following identity but as I couldn't do it I wonder if it is true? $$\frac{\cot^2\frac{α}{2}-\cot\frac{3α}{2}}{\cos^2\frac{α}{2}\cosα(1+\cot^2\frac{3α}{2})}=8$$
0
votes
3answers
56 views

Solving trigonometric expressions in $x$

I am having problems understanding how to write an algebraic expression in $x$ for: $$\sin\left(\arcsin(x)-\arctan\left(\frac{2}{x}\right)\right)$$
0
votes
1answer
30 views

The period of a non-linear pendulum

The period of a non-linear pendulum is $T = \sqrt{2} \cdot \int_{-\theta_0}^{\theta_0} \frac{d{\theta}}{\sqrt{\cos(\theta) - \cos(\theta_0)}}$. My problem: what will happened with the period $T$, ...
0
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1answer
49 views

Solving double angle trigonometric equities [on hold]

I am having problems understanding how to solve the equation: $\sin{(2x)} = \sin{(x)}\cos{(x)}^{1/2}$
-1
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1answer
34 views

Inverse trigonometric function problem [on hold]

Please prove this easy way. I tried it by solving right hand side but it didn't go well. $$ 2\cos^{-1} \frac45 = \sin^{-1} \frac{24}{25} $$
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0answers
30 views

Trigonometric equation of 4 answer

$3\tan(2x+22)= -6.339$ $\tan(2x+22)= -2.113$ $2x+22=-64.67$ $x=-43.33$ $x=180-43.33$, $x=360-43.33$ $x=136.67$, $x=316.67$ How to find another two answer ?
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3answers
30 views

Inverse trignometric proof? [on hold]

Please help me prove the following : $$ \cos^{-1}\frac{63}{65} + 2\tan^{-1}\frac15 = \sin^{-1}\frac35 $$
1
vote
3answers
54 views

Solve these equations simultaneously (trig)

Solve for $ x,y: $ \begin{equation}\cos x -\cos(x+y) = 0 \end{equation} \begin{equation}\cos y -\cos(x+y) = 0 \end{equation} The answers are $(0, 0), (\frac{2\pi}{3}, \frac{2\pi}{3})$. I get ...
1
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2answers
47 views

Proving trigonometric identity $\frac{1+\sin x}{1-\sin x}-\frac{1-\sin x}{1+\sin x}=4\sec x \tan x$ [on hold]

This is a trigonometry question that i did not quite understand very well. Show that $$\frac{1+\sin x}{1-\sin x}-\frac{1-\sin x}{1+\sin x}=4\sec x \tan x$$
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1answer
31 views

The graph of tan(sec(x))

A lot of the trig_function(trig_function(x)) look something like this, with asymptotes that have infinite (?) oscillating (?) lines infinitely approaching them ...
-1
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2answers
62 views

How to Calculate csc(2.85) in Calculator?

In my calculator (TI-84), there are only $sin, cos,$ and $tan$ commands (and inverse sin, inverse cos, inverse tan). I had a question that was as follows: Calculate $csc(2.85)$ in which I was ...
2
votes
1answer
51 views

How we can find the sign for trigonometric functions without graph

For $\sin(x)$ or $\cos(x)$ etc. how we can show that it is negative on $\left[\pi ,2\pi \right]$ ? without graph? So if we have $\sin(2x)$ or $\cos(2x)$ how we can find the sign on $\left[0,2\pi ...
1
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3answers
50 views

Integral of a tangent function

$$ \displaystyle {\int_{0}^{z}} \sqrt {1 + \tan^2(\dfrac{\pi}{4} \dfrac{z}{H} )} dz $$ _ $$ gives $$ _ $$ \dfrac{4H}{\pi} {\sinh^{-1}} ( {\tan \dfrac{\pi}{4} \dfrac{z}{H} } ) $$ Please advise ...
0
votes
1answer
34 views

Why this formula used ? angle = (2π- 2πθ/255.0); [on hold]

i got a source code regarding reading a minutia from an iso standard, now i need to create another code to save the minutia in the same ...
1
vote
1answer
39 views

Infinite summation of a trigonometric series

$\sum_{n=1}^{n=\infty}\sin(\frac{n\pi x}{L})\sin(\frac{n\pi y}{L})\surd(k^2+\frac{n^2 \pi^2}{L^2})$ I am trying to solve the above summation. I still could not figure out if this summation converges ...
0
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1answer
36 views

Finding speed of snowballs given initial velocity and angles

You and a friend stand on a snow-covered roof. You both throw snowballs from an elevation of $14$ m with the same initial speed of $12$ m/s, but in different directions. You throw your snowball ...
1
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1answer
12 views

How can I find the inner limit of a line passing through a lune?

I have a crescent defined by two offset circles with different radii: a small one (let's call it outer circle) centered at (0,0) with radius ...
1
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2answers
51 views

Is $\log_{\cos x}(1)$ defined at $x=0+2k\pi$? [duplicate]

I have an equation like this: $\cos(x) ^ {\sin(x)} = 1$ I thought I would solve it like this: $\cos(x) ^ {\sin(x)} = 1$ $\sin(x) = \log_{\cos(x)}(1)$ $\sin(x) = 0 $ $x = 0+k\pi$ But I'm ...
6
votes
4answers
195 views

In a 30-60 right triangle the side opposite the 30 degree angle is half the length of the hypotenuse. Why? [on hold]

In a 30-60 right triangle the side opposite the 30 degree angle is half the length of the hypotenuse. A statement from the trigonometry section of Simmons' Precalculus in a nutshell. Please ...
2
votes
2answers
58 views

Volume of a parallelepiped, given 8 vertices

Given the eight vertices $(0,0,0)$, $(3,0,0)$, $(0,5,1)$, $(3,5,1)$, $(2,0,5)$, $(5,0,5)$, $(2,5,6)$, and $(5,5,6)$, find the volume of the parallelepiped. I'm having trouble finding the 1 vertex ...
-2
votes
2answers
55 views

$\int _{k\pi }^{\left(k+1\right)\pi }\:\left|\sin\left(x\right)\right|dx$ [on hold]

How can I solve the following integral? $\int _{k\pi }^{\left(k+1\right)\pi }\:\left|\sin\left(x\right)\right|dx$
2
votes
2answers
43 views

Proving the Derivative of cosine and sine functions

In the proof of the derivatives of cosine and sine functions, we used the facts that: $$\lim\limits_{\Delta x \to 0} \frac{\cos \Delta x - 1}{\Delta x} = 0$$ and $$\lim\limits_{\Delta x \to 0} ...
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0answers
27 views

(sin10+sin50+sin130)/sin80 = ? Solution please [on hold]

$\frac{\sin10+\sin50+\sin130}{\sin80}$= ? Solution please, Thanks in advance
0
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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 ...
7
votes
4answers
361 views

How to construct a line with a given equal distance from 3 Points in 3 Dimensions?

Important: I'm now convinced that 4 points are needes in order to reduce the solutions to a finite number. (Which is necessary because I need ALL solutions) In a computer science context I need to ...
0
votes
1answer
29 views

Requirements for learning and understanding trigonometry?

Im reaching a point in programing where I need to create basic shapes which I simply cant since my math skills are very bad. After finding out that the skills required are trigonometry I read a few ...
3
votes
1answer
68 views

Evaluating: $I_1 = \sin^{-1} \left(\sqrt{\frac{x}{x+a}}\;\right) $

$$I_1 =\int \sin^{-1} \left(\sqrt{\frac{x}{x+a}}\;\right) dx= ?$$ I tried substitution: $\sin^{-1} \left(\sqrt{\frac{x}{x+a}}\;\right) = \Xi$, but then I'm not able to do anything after the resulting ...
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votes
2answers
23 views

to find the value of angle A in the given equation

4 sin A cos A = 1 - 2 sin A + 2 cos A I could not find the value of either sin A or cos A in the above equation. So please direct me on how to find the values of ...
2
votes
2answers
57 views

Squeeze Theorem: $\lim_{x\to 0} \, \frac{x^2}{\sin ^2(x)}$

I'm having a hell of a time understanding how to apply the Squeeze Theorem and the corresponding theorems to solving problems like the following. $\lim_{x\to 0} \, \frac{x^2}{\sin ^2(x)}$ So I can ...
0
votes
1answer
32 views

Given $\tan x +\cot x = 3$ and $x$ is in first quadrant. Find $\sin x$.

Simplifying, I have $$\frac{1}{\sin x\cdot \cos x} = 3$$ I have tried many manipulations but did not get the answer. Point me the right direction to the solution. (This problem is in the beginning ...
0
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0answers
17 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 ...
1
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1answer
42 views

Sine Sum : Inverse Circular Function Proof

It is known that the following holds good: $$ \sin^{-1} x + \sin^{-1}y \\ \begin{align} &=\sin^{-1}( x\sqrt{1-y^2} + y\sqrt{1-x^2}) \;\;;x^2+y^2 \le 1 \;\text{ or }\; x^2+y^2 > 1, xy< 0\\ ...
-5
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1answer
47 views

How to Prove this mathematical expression???? [on hold]

We know x isn't equal ninety degree . How to prove this ????????? $$ 1/\cot^6x - 3\tan^2x/\cos^2x = 1 + \tan^6x $$ Please describes step by step. Thanks.
5
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1answer
84 views

Find the value of $\sum_{m=1}^\infty tan ^ {-1}\frac{2m}{m^4+m^2+2}$

How to find value of this sum? $$\sum\limits_{m=1}^\infty \tan^{-1}\left(\frac{2m}{m^4+m^2+2}\right)$$ I can't understand how to simplify this. Should I use any trigonometric substitution to simplify ...
0
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0answers
34 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 ...
2
votes
3answers
51 views

Determine height/width of rectangle in perspective

I have the following situation. I've got a 2d plane in which I have drawn a rectangle (red). This is done by picking a point (big red dot), and using the vanishing points calculated by some other ...
0
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2answers
30 views

Trisecting a line in the complex plane

We have $x = 11-13i$ and $y = 35-i$. $a$ is a complex number which trisects the line segment joining $x$ and $y$. $a$ is also closer to $x$ than $y$. Find $a$. I'm not sure where to start. Would a ...
0
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1answer
19 views

Get angle in degrees of coordinate on circle.

So assume I have coordinates of two points on a circle, and the coordinate of the center of the circle. How would I go about finding the angle of the points in degrees?
4
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3answers
363 views

Approximation of the Sine function near $0$

What is the reason that for $x<0.5$, $\sin(x)\approx x$? Are there more known properties of these kind for other trigonometry functions?
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3answers
45 views

Proving algebraic equations with circle theorems

I got as far as stating that OBP=90˚ (as angle between tangent and radius is always 90˚), and thus CBO=90˚- 2x. CBO=OCB as they are bases in a isosceles. COB=180-90-2x-90-2x. But after this, i am ...
1
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0answers
41 views

Prove that these result are the same

I did this trigonometric integral in two different ways, and the results that I got were with two different trigonometric functions, $\sec x$ and $\tan x$. The integral is: $\mathbf{\int tan^{5}x \, ...
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votes
1answer
25 views

The asymptote of $y=\mathrm{sinc}(t)$ as time increases

Is there any known approximate formula that maps decay percentage of $\mathrm{sinc}(t)$ with decaying time? Or in other words, is there a known asymptote of $y=\mathrm{sinc}(t)$ as time increases?
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1answer
30 views

Calculate the area between functions

[I need to find the area between this three functions, therefore I need to use Integral g(x)-f(x) but I tried and it gives me negative and enormous numbers.]