# Tagged Questions

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

49 views

77 views

### Is there a sequence of $v_{n}$ such that $G=\prod_{n=1}^{\infty} \frac{2\tan^{-1}(v_{n})}{\pi}> 1$?

Let $G=\prod_{n=1}^{\infty} \frac{2\tan^{-1}(v_{n})}{\pi}$, where $v_{n}$ is an increasing, monotonic sequence of natural numbers: is it true that there is no sequence of $v_{n}\in\mathbb{N}$ such ...
505 views

### Prove $\alpha \in\mathbb R$ is irrational, when $\cos(\alpha \pi) = \frac{1}{3}$

I am trying to prove: If $\cos(\pi\alpha) = \frac{1}{3}$ then $\alpha \in \mathbb{R} \setminus \mathbb{Q}$ So far, I've tried making it into an exponential, since exponentials are easier to ...
39 views

### How do I compute the angles of a pyramid from the angle between its sides?

I have been given the following problem to solve: In a right pyramid whose base is an equilateral triangle, the angle between 2 side-faces is 70 degrees. Compute the base angle of a side-face. I ...
465 views

### Fixed-Point Iteration method unable to converge to any of a function's infinte roots

An equation is given to me which has to be solved by direct iteration method: $$\sin(x) = {x+1 \over x-1}$$ or $$f(x)=\sin(x)-{x+1 \over x-1} = 0$$ I follow the following procedure with reasons ...
37 views

### If $\frac{m+1}{m-1}=\frac{cos(\alpha-\beta)}{sin(\alpha+\beta)}$„ then

If $$\frac{m+1}{m-1}=\frac{\cos(\alpha-\beta)}{\sin(\alpha+\beta)}$$, prove that : $$m=\tan(π/4 +\alpha).\tan(π/4 +\beta)$$. My attempts/ Here .. ...
917 views

### Elementary Proof of Euler's Sine Expansion $\prod_{k=1}^\infty\left({1-\frac{x^2}{k^2\pi^2}}\right)$

I've been looking at proofs of Euler's sine expansion, that is $$\frac{\sin x}{x}=\prod_{k=1}^\infty\left({1-\frac{x^2}{k^2\pi^2}}\right)$$ All the proofs seem to rely on complex analysis and ...
20 views

25 views

31 views

### Showing that $\alpha$ satisfies the equation $\sin 2x=x$

This is an A level question. For better understanding, I will attach a screenshot of the question and the mark scheme. Question: Here's what I have done: $$A(OBA) = \frac 12r^2α$$ [basic ...
29 views

### What is this procedure called for angle radians?

So, my lecturer says that $-\cos(\frac{\pi}{8}) = \cos(\frac{9\pi}{8})$. What did he do to get that? Please recommend a source where I can brush up on my knowledge of angles.
52 views

### How does $\frac{\sin\theta}{\cos\theta}$ become $\frac{y}{x}$

I ended up in the wrong math class (trigonometry) for my level but am trying to survive by catching up on some more basic principles. I'm wondering if the same principle (and if so, what is it) is ...
49 views

### Evaluate the definite integral $\int_{0}^{a}\frac{dx}{(a^2+x^2)^{3/2}}$

I'm trying to solve this integral with trigonometric substitution but am having a ton of trouble: $$\int\limits_{0}^{a}{\frac{dx}{(a^2+x^2)^{\frac{3}{2}}}}$$ I tried $x=a\tan{\theta}$ and thus ...
23 views

### Trigonometry markup

Imagine we have the following problem; $$\cos(x) = \cos(a) \Rightarrow x=a+k\times 2\pi\\ or \\x=-a+k\times 2\pi$$ And we have the following answers.. : $$a=\frac{\pi}{3} \\or \\a=-\frac{\pi}{3}$$ ...
20 views

### How do you calculate the change in thickness of a cylinder, if you shave off a flat section?

I have a piece of steel, cylindrical (hollow), 200mm outside diameter with 160mm inside diameter (...
43 views

30 views

64 views

### Proof that there are no solutions this equation. (3 variables, Square root and Sine) [on hold]

Hypothesis: There do not exist three different positive integers $a,b,c$ such that $$-\sqrt{ab}\cdot \sin(p \cdot (a-b))+\sqrt{ac}\cdot \sin(p \cdot (a-c)) -\sqrt{bc}\cdot \sin(p \cdot (b-c)) =0$$ ...
24 views

### Rational solutions for $\sin(n)$ in radians

This is completely for my own curiosity. Does $y = \sin(n)$ have rational solutions for $n$, an integer number of radians. I know that this is strange because usually integers are only used in ...
122 views

### Why is $s$ used for arc length?

Why is $s$ used for arc length? I looked around online, but I can't find a definite answer. Thank you!
34 views

### Find elevator height given rope length?

This question is deceptively difficult. I feel like it's probably some classic example somewhere, but I'm not sure how to describe it in enough detail to get valid results in searching online. ...
29 views

### Find the $sin$ of an angle $B$ using law of sines given side angle side

this is giving me trouble, here's what I've tried: Q.A triangle has sides $a=2$, $b=3$, and $\angle C = 60^o$. Using the law of sines, find $\sin(B)$ OK so I know the law of sines is: ...
6k views

### How to solve $4\sin \theta +3\cos \theta = 5$

Another problem that I already wasted hours on. Given $$4\sinθ +3\cosθ = 5$$ Find $$4\cosθ -3\sinθ$$ Help me guys (PS:I'm not that good in maths)
356 views

### Finding Y coordinate of third triangle point when X coordinate and two other points are already known

Suppose you know the coordinates for points A and B of a triangle. We can refer to those coordinates as (Ay,Ax) and (By,Bx). Also, suppose you know the X coordinate for point C (Cx) but do not know ...
Please prove (or disprove, and give the correct answer): $$2 =\mathrm{argmax}_{r\geq 1}\min_{x\in \mathbb{R}}\left[\cos\left(x\right)+\cos\left(rx\right)\right]$$ In other words, find $r \geq 1$, ...