Question

$\sum_{n=0}^{\infty} \frac{\sin(nx)}{3^n}$

score 608 · Answer 1 · 2026-04-09 13:09:40

608

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$\sum_{n=0}^{\infty} \frac{\sin(nx)}{3^n}$

Published on 09 Apr 2026 - 13:09

score 97 · Answer 2 · 2026-04-15 18:10:00

97

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Complex proof for “a curious property of regular heptagons”: $\frac{1}{A_1A_2} = \frac{1}{A_1A_3} + \frac{1}{A_1A_4}$

Published on 15 Apr 2026 - 18:10

score 75 · Answer 3 · 2026-04-15 19:55:33

75

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Find the derivative of $\arctan \left( \cos x\over1+\sin x \right)$.

Published on 15 Apr 2026 - 19:55

score 71 · Answer 4 · 2026-04-16 04:57:14

Define a rectangle with one edge of known length and whose two opposing corners are tangent to two circles of known size and location.

score 58 · Answer 5 · 2026-04-12 09:44:57

58

Views

How to obtain the analytic representation of the given infinite series?

Published on 12 Apr 2026 - 9:44

score 412 · Answer 6 · 2026-04-16 10:50:23

412

Views

The origin of the Fibonacci sequence and the metallic means or silver means (also ratios or constants)

Published on 16 Apr 2026 - 10:50

score 136 · Answer 7 · 2026-04-15 23:59:11

136

Views

Minimizing $9 \sec^2{x} + 16 \csc^2{x}$

Published on 15 Apr 2026 - 23:59

score 117 · Answer 8 · 2026-04-12 04:49:18

117

Views

Real solutions of a cosx + b sinx = k

Published on 12 Apr 2026 - 4:49

score 126 · Answer 9 · 2026-04-11 20:55:01

126

Views

How are these two solutions for $\int \cot x\,dx$ equivalent?

Published on 11 Apr 2026 - 20:55

score 73 · Answer 10 · 2026-04-15 00:38:30

73

Views

If $x\sin A=y\sin(A+2π/3) =z\sin(A+4π/3),$ derive a relation among $x, y, z$ by eliminating $A$

Published on 15 Apr 2026 - 0:38

score 341 · Answer 11 · 2026-04-16 13:32:05

341

Views

Why does $\int_{-\infty}^{+\infty }\arctan\left(\frac{1}{1+x^2}\right)dx$ have a real value when the indefinite integral uses $i$?

Published on 16 Apr 2026 - 13:32

score 160 · Answer 12 · 2026-04-15 15:56:49

160

Views

Solve the inequality $\sin x > \ln x$

Published on 15 Apr 2026 - 15:56

score 72 · Answer 13 · 2026-04-17 02:48:33

72

Views

Proving $\tan\left(x+\frac{\pi}{3}\right) = \frac{4\tan x+\sqrt{3}\sec^2x}{\sec^2x-4\tan^2x}$

Published on 17 Apr 2026 - 2:48

score 85 · Answer 14 · 2026-04-15 23:15:49

85

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$\sqrt2 x^2 - \sqrt3 x + k = 0$ with solutions $\sin \theta , \cos \theta$

Published on 15 Apr 2026 - 23:15

score 107 · Answer 15 · 2026-04-16 11:27:12

107

Views

$x+y = 120^\circ, x\geq 0, y\geq 0.$ max and min of $\sin x + \sin y$

Published on 16 Apr 2026 - 11:27

List Question

$\sum_{n=0}^{\infty} \frac{\sin(nx)}{3^n}$

Complex proof for “a curious property of regular heptagons”: $\frac{1}{A_1A_2} = \frac{1}{A_1A_3} + \frac{1}{A_1A_4}$

Find the derivative of $\arctan \left( \cos x\over1+\sin x \right)$.

Define a rectangle with one edge of known length and whose two opposing corners are tangent to two circles of known size and location.

How to obtain the analytic representation of the given infinite series?

The origin of the Fibonacci sequence and the metallic means or silver means (also ratios or constants)

Minimizing $9 \sec^2{x} + 16 \csc^2{x}$

Real solutions of a cosx + b sinx = k

How are these two solutions for $\int \cot x\,dx$ equivalent?

If $x\sin A=y\sin(A+2π/3) =z\sin(A+4π/3),$ derive a relation among $x, y, z$ by eliminating $A$

Why does $\int_{-\infty}^{+\infty }\arctan\left(\frac{1}{1+x^2}\right)dx$ have a real value when the indefinite integral uses $i$?

Solve the inequality $\sin x > \ln x$

Proving $\tan\left(x+\frac{\pi}{3}\right) = \frac{4\tan x+\sqrt{3}\sec^2x}{\sec^2x-4\tan^2x}$

$\sqrt2 x^2 - \sqrt3 x + k = 0$ with solutions $\sin \theta , \cos \theta$

$x+y = 120^\circ, x\geq 0, y\geq 0.$ max and min of $\sin x + \sin y$

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