Question

Proof that $\arctan z+\arctan \frac{1}{z}$ does not depend on $\operatorname{Im}z$ when $\operatorname{Re}z\ne 0$ and $\operatorname{Im}z\ne 0$

score 90 · Answer 1 · 2026-04-13 04:07:45

90

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Proof that $\arctan z+\arctan \frac{1}{z}$ does not depend on $\operatorname{Im}z$ when $\operatorname{Re}z\ne 0$ and $\operatorname{Im}z\ne 0$

Published on 13 Apr 2026 - 4:07

score 168 · Answer 2 · 2026-04-13 19:14:39

168

Views

Find the minimum positive root of $\sin{3x}=a$ ($a>0)$, given that there exist two roots differing by $\frac{\pi}{4}$.

Published on 13 Apr 2026 - 19:14

score 111 · Answer 3 · 2026-04-11 03:58:54

111

Views

A Puzzle From Hobson's Plane Trigonometry

Published on 11 Apr 2026 - 3:58

score 554 · Answer 4 · 2026-04-15 16:09:22

554

Views

How to show that $\int_{0}^{\frac{\pi}{4}}\ln(\sqrt{\tan x}+\sqrt{\cot x} -\sqrt{2})\ dx=0$

Published on 15 Apr 2026 - 16:09

score 41 · Answer 5 · 2026-04-09 22:09:09

41

Views

Trigonometry calculation doubt

Published on 09 Apr 2026 - 22:09

score 410 · Answer 6 · 2026-04-17 01:33:29

410

Views

Find the measure of an angle

Published on 17 Apr 2026 - 1:33

score 103 · Answer 7 · 2026-04-14 10:51:16

103

Views

Prove $\sin(a) < a < \tan(a)$ when $0 < a < \pi/2$

Published on 14 Apr 2026 - 10:51

score 93 · Answer 8 · 2026-04-11 01:32:48

93

Views

Calculating Range of a Function

Published on 11 Apr 2026 - 1:32

score 54 · Answer 9 · 2026-04-16 14:14:10

54

Views

Solve $\cos(a)+\cos(b)=\cos(c)+\cos(d)$ for $a, b, c, d\in(0, \pi)$.

Published on 16 Apr 2026 - 14:14

score 86 · Answer 10 · 2026-04-12 22:52:52

86

Views

How can I solve $\cos A = -\frac12$ without having to consult a table of angles and their cosines?

Published on 12 Apr 2026 - 22:52

score 54 · Answer 11 · 2026-04-14 22:34:54

54

Views

Calculating a point's position on a line so the angle of two segments are equal.

Published on 14 Apr 2026 - 22:34

score 101 · Answer 12 · 2026-05-05 13:41:17

101

Views

Derive formula for the area of triangle provided that you know 2 angles and side between them.

Published on 05 May 2026 - 13:41

score 83 · Answer 13 · 2026-04-11 06:18:48

83

Views

Inscribed Equilateral Triangle Trig - Expression for P/A

Published on 11 Apr 2026 - 6:18

score 56 · Answer 14 · 2026-04-15 05:43:30

56

Views

How do I sketch $y = -2\sin\big(2(x+\frac{π}{6})\big)+1$ between $[-π,π]$ without any fuss?

Published on 15 Apr 2026 - 5:43

score 1.5k · Answer 15 · 2026-04-10 07:13:24

1.5k

Views

Finding angle between two points on circle given cartesian coordinates of the points

Published on 10 Apr 2026 - 7:13

List Question

Proof that $\arctan z+\arctan \frac{1}{z}$ does not depend on $\operatorname{Im}z$ when $\operatorname{Re}z\ne 0$ and $\operatorname{Im}z\ne 0$

Find the minimum positive root of $\sin{3x}=a$ ($a>0)$, given that there exist two roots differing by $\frac{\pi}{4}$.

A Puzzle From Hobson's Plane Trigonometry

How to show that $\int_{0}^{\frac{\pi}{4}}\ln(\sqrt{\tan x}+\sqrt{\cot x} -\sqrt{2})\ dx=0$

Trigonometry calculation doubt

Find the measure of an angle

Prove $\sin(a) < a < \tan(a)$ when $0 < a < \pi/2$

Calculating Range of a Function

Solve $\cos(a)+\cos(b)=\cos(c)+\cos(d)$ for $a, b, c, d\in(0, \pi)$.

How can I solve $\cos A = -\frac12$ without having to consult a table of angles and their cosines?

Calculating a point's position on a line so the angle of two segments are equal.

Derive formula for the area of triangle provided that you know 2 angles and side between them.

Inscribed Equilateral Triangle Trig - Expression for P/A

How do I sketch $y = -2\sin\big(2(x+\frac{π}{6})\big)+1$ between $[-π,π]$ without any fuss?

Finding angle between two points on circle given cartesian coordinates of the points

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