Tagged Questions
1
vote
2answers
85 views
How do i prove that $\frac{1}{\pi} \arccos(1/3)$ is irrational?
How do i prove that $\frac{1}{\pi} \arccos(1/3)$
is irrational?
3
votes
2answers
63 views
Define two rational numbers $\alpha$ and $x$ such that $\sin( { \alpha }) =x$
Of course for $x\neq 0 $ and $\alpha$ in radians. Can you define them?
6
votes
3answers
147 views
Prove that the Tangent of 75 degrees equals 2 plus the square-root of 3
My (very simple) question to a friend was how do I prove the following using basic trig principles:
$\tan75^\circ = 2 + \sqrt{3}$
He gave this proof (via a text message!)
$1. \tan75^\circ$
$2. = ...
10
votes
2answers
270 views
Is sin(x) necessarily irrational where x is rational?
My friend and I were discussing this and we couldn't figure out how to prove it one way or another.
The only rational values I can figure out for $\sin(x)$ (or $\cos(x)$, etc...) come about when $x$ ...
31
votes
6answers
2k views
$\sin 1^\circ$ is irrational but how do I prove it in a slick way? And $\tan(1^\circ)$ is …
In the book 101 problems in Trigonometry, Prof. Titu Andreescu and Prof. Feng asks for the proof the fact that $\cos 1^\circ$ is irrational and he proves it. The proof proceeds by contradiction and ...
0
votes
1answer
173 views
When are $\theta$ and $\sin\theta^\circ$ both rational? [duplicate]
Possible Duplicate:
Sine values being rational
I'm guessing that if I look in Ivan Niven's elementary book on irrational numbers, I'll find the answer to this quickly, but I'm posting it ...
3
votes
4answers
997 views
When is $\sin(x)$ rational?
Obviously, there are some points (like $\pi,30$) but I am unsure if there are more.
How can it be proved that there are no more points, or what those points will be?
EDIT: I largely meant to ask ...
12
votes
2answers
1k views
ArcTan(2) a rational multiple of $\pi$?
Consider a $2 \times 1$ rectangle split by a diagonal. Then the two angles
at a corner are ArcTan(2) and ArcTan(1/2), which are about $63.4^\circ$ and $26.6^\circ$.
Of course the sum of these angles ...
4
votes
1answer
236 views
rational angles with sines expressible with radicals
An angle x is rational when measured in degrees. sin(x) is can be written using radicals. What are the conditions on x? If nested square roots are allowed?
What I know so far:
If sin(x) can be ...
3
votes
1answer
220 views
How can I determine a number is irrational?
I have a hypothesis about regular polygons, but in order to prove or disprove it I need a way to determine whether an expression is rational. Once I boil down my expression the only part that could be ...
4
votes
1answer
485 views
Sine values being rational
Can $$\sin r\pi $$ be rational if $r$ is irrational? Either a direct or existence proof is fine.
