Question

Is this a True Property of the Lemniscate of Bernoulli?

score 189 · Answer 1 · 2026-04-13 21:40:29

189

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Is this a True Property of the Lemniscate of Bernoulli?

Published on 13 Apr 2026 - 21:40

score 46 · Answer 2 · 2026-04-15 22:30:23

46

Views

Find number of possible values satisfying $\cos \left(\pi\sqrt{x-4}\right)\cos \left(\pi\sqrt{x}\right)=1$

Published on 15 Apr 2026 - 22:30

score 69 · Answer 3 · 2026-04-15 07:15:42

69

Views

Roots of equation involving both polynomials and trigonometric functions

Published on 15 Apr 2026 - 7:15

score 46 · Answer 4 · 2026-04-11 16:45:39

46

Views

Number of solutions to a given equation

Published on 11 Apr 2026 - 16:45

score 1.6k · Answer 5 · 2026-04-12 13:40:04

1.6k

Views

Geometric justification of a rotation matrix

Published on 12 Apr 2026 - 13:40

score 277 · Answer 6 · 2026-04-15 23:27:39

277

Views

Atypical way to find angle between unit vectors: $\theta = 2 \sin^{-1}\left(\frac{1}{2}\left\|\hat{A}-\hat{B}\right\|\right)$

Published on 15 Apr 2026 - 23:27

score 165 · Answer 7 · 2026-04-14 19:35:54

165

Views

Sum of Cosine Waves

Published on 14 Apr 2026 - 19:35

score 67 · Answer 8 · 2026-04-09 23:28:52

67

Views

Help explaining the simplification of an integral

Published on 09 Apr 2026 - 23:28

score 61 · Answer 9 · 2026-04-11 11:59:02

61

Views

Existence of basis of solution

Published on 11 Apr 2026 - 11:59

score 603 · Answer 10 · 2026-04-13 10:27:52

603

Views

Tracking the movement of the watch hand

Published on 13 Apr 2026 - 10:27

score 341 · Answer 11 · 2026-04-16 04:17:45

Showing that $\cos^p{\Theta} \le \cos{p\Theta}$, for $0<\Theta<\frac{\pi}{2}$ and $0<p<1$, by analyzing $f(\theta)=\frac{\cos^p\Theta}{\cos p\Theta}$

score 129 · Answer 12 · 2026-04-16 00:03:13

129

Views

How does $\frac{1-\cos x}{1+\cos x}$ become $\frac{2\sin^2(x/2)}{2\cos^2(x/2)}$?

Published on 16 Apr 2026 - 0:03

score 60 · Answer 13 · 2026-04-15 05:57:29

60

Views

Show $\langle x-Px,y-Px\rangle \leq 0$ for $Px$ the projection of $x$ onto $C$ convex, and any $y \in C$.

Published on 15 Apr 2026 - 5:57

score 96 · Answer 14 · 2026-04-12 12:24:25

96

Views

Using ratiotest to check convergence of $\sum \sin(\frac{1}{n!})$.

Published on 12 Apr 2026 - 12:24

score 242 · Answer 15 · 2026-04-14 11:18:23

242

Views

Computing $\sum_{k=0}^n{2n\choose 2k}(-1)^k\sin^{2k}\theta\cos^{2n-2k}\theta$ using Euler's formula

Published on 14 Apr 2026 - 11:18

List Question

Is this a True Property of the Lemniscate of Bernoulli?

Find number of possible values satisfying $\cos \left(\pi\sqrt{x-4}\right)\cos \left(\pi\sqrt{x}\right)=1$

Roots of equation involving both polynomials and trigonometric functions

Number of solutions to a given equation

Geometric justification of a rotation matrix

Atypical way to find angle between unit vectors: $\theta = 2 \sin^{-1}\left(\frac{1}{2}\left\|\hat{A}-\hat{B}\right\|\right)$

Sum of Cosine Waves

Help explaining the simplification of an integral

Existence of basis of solution

Tracking the movement of the watch hand

Showing that $\cos^p{\Theta} \le \cos{p\Theta}$, for $0<\Theta<\frac{\pi}{2}$ and $0<p<1$, by analyzing $f(\theta)=\frac{\cos^p\Theta}{\cos p\Theta}$

How does $\frac{1-\cos x}{1+\cos x}$ become $\frac{2\sin^2(x/2)}{2\cos^2(x/2)}$?

Show $\langle x-Px,y-Px\rangle \leq 0$ for $Px$ the projection of $x$ onto $C$ convex, and any $y \in C$.

Using ratiotest to check convergence of $\sum \sin(\frac{1}{n!})$.

Computing $\sum_{k=0}^n{2n\choose 2k}(-1)^k\sin^{2k}\theta\cos^{2n-2k}\theta$ using Euler's formula

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