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$What is $\sin^2(x)$ equal to?$

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What is $\sin^2(x)$ equal to?

Let's take the sine of $30^\circ$ which is one-half. If you take $\sin^2(30^\circ)$, would that just be the sine of $900$? Or would it be equal to on...

Published: Aug 14, 2026

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Sphere eversion and inversion

the following things are asked because of a research I am doing for a short novel that I am writing. It contains only very little mathematics, however I w...

Published: Aug 14, 2026

$Show that $\int_{[0,1]\times [0,1]}\frac{dx \, dy}{1-xy} = \frac{\pi^2}{6}$$

updates

Show that $\int_{[0,1]\times [0,1]}\frac{dx \, dy}{1-xy} = \frac{\pi^2}{6}$

$$ \int_{[0,1] \times [0,1]} \frac{dx \, dy}{1-xy}=\frac{\pi^2}{6}, $$ there is a hint for substitution given but I can't seem to get anywhere with i...

Published: Aug 14, 2026

$Questions concerning smallest fraction between two given fractions.$

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Questions concerning smallest fraction between two given fractions.

I recently encountered this on a practice test Find the smallest positive integer $n$ such that there exists an integer $m$ satisfying $0.33 < \frac{m}...

Published: Aug 14, 2026

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How to solve this simple Algebraic equation? (Wolfram & SymboLab both stumped...)

I need to solve the following equation for a hobby coding project I'm working on and I can't figure out the solution. Wolfram and SymboLab solve...

Published: Aug 14, 2026

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Discriminant of Elliptic Curves

In the study of elliptic curves, specifically in Weierstrass form, you have the equation $E : y^2 = x^3 +ax +b$. However I have found the discriminant com...

Published: Aug 14, 2026

$Two independent events, $A$ and $B$; find $B$ given only $A$ and $A\cup B$$

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Two independent events, $A$ and $B$; find $B$ given only $A$ and $A\cup B$

Sorry to be a burden but my maths exam is tomorrow and I have no idea how to do this at all. Here is the exact question : The two independent events $A$ a...

Published: Aug 14, 2026

general

Find the 3 angles of the hyperbolic triangle

A(0,5) B(0,2) C(4,2) In Euclidean geometry the three points given are the vertices of a right-angled triangle. Find the three angles of the hyperbolic tri...

Published: Aug 14, 2026

$Definition of minor for a general $m \times n$ matrix.$

updates

Definition of minor for a general $m \times n$ matrix.

Following is the definition of minor given in the text : For a matrix $A$, consider its $k × k$ submatrix, obtained by taking $k$ rows and $k$ columns. Th...

Published: Aug 14, 2026

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What is a null set?

I am very confused with null sets. I get that a set which has no elements will be called a null set but I am not getting the examples given below. Please ...

Published: Aug 14, 2026

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