Question

Showing that $ \int_0^\pi \frac{\sin{(kx)}}{\sin(x)} d x = \pi $ for odd integer $k$

score 1.2k · Answer 1 · 2026-04-16 00:14:28

1.2k

Views

Showing that $ \int_0^\pi \frac{\sin{(kx)}}{\sin(x)} d x = \pi $ for odd integer $k$

Published on 16 Apr 2026 - 0:14

score 2.4k · Answer 2 · 2026-04-15 23:47:39

2.4k

Views

Why does $\sin(x) - \sin(y)=2 \cos(\frac{x+y}{2}) \sin(\frac{x-y}{2})$?

Published on 15 Apr 2026 - 23:47

score 1.4k · Answer 3 · 2026-04-16 22:13:36

1.4k

Views

$x^2 + y^2+xy = 1$ , then find the minimum of $x^3 y + xy^3 +4$

Published on 16 Apr 2026 - 22:13

score 958 · Answer 4 · 2026-04-16 00:16:52

958

Views

$\sin x+\sin y+\sin z=4\cos\frac{x}{2}\cos\frac{y}{2}\cos\frac{z}{2}$

Published on 16 Apr 2026 - 0:16

score 138 · Answer 5 · 2026-04-16 09:45:05

138

Views

Solutions to $(x-x_0)\cos(x_0)+\sin(x_0)-\sin(x)=0$

Published on 16 Apr 2026 - 9:45

score 159 · Answer 6 · 2026-04-16 11:45:37

159

Views

If $a\sin^2\theta-b\cos^2\theta=a-b$, then prove $a\cos^4\theta+b\sin^4\theta=\frac{ab}{a+b}$

Published on 16 Apr 2026 - 11:45

score 75 · Answer 7 · 2026-04-12 09:12:39

75

Views

Calculating Arc Hyperbolic CoSecant faster than using a standard power series

Published on 12 Apr 2026 - 9:12

score 5.7k · Answer 8 · 2026-04-16 23:37:58

5.7k

Views

Fourier Series for $\cos^3(x)$

Published on 16 Apr 2026 - 23:37

score 687 · Answer 9 · 2026-04-13 04:15:24

687

Views

Finding a point on a circle in 3D space which is a given distance away from another point

Published on 13 Apr 2026 - 4:15

score 210 · Answer 10 · 2026-04-15 14:05:27

210

Views

Sum this series: $1+\cos{\theta}\sec{\theta}+\cos{2\theta}\sec^2{\theta}+\cdots+\cos{n\theta}\sec^n{\theta}$

Published on 15 Apr 2026 - 14:05

score 44 · Answer 11 · 2026-03-25 22:03:10

44

Views

Sums of trigonometric functions and polynomials

Published on 25 Mar 2026 - 22:03

score 412 · Answer 12 · 2026-04-13 23:13:28

412

Views

integral of $\sec x \tan x$

Published on 13 Apr 2026 - 23:13

score 54 · Answer 13 · 2026-04-15 13:19:55

54

Views

If $(1-\cos{x})^{n+1}=\sum_{k=0}^\infty c_k\cos{kt}$ for some integers $c_k$, then what is $\sum_{k=0}^\infty kc_k$?

Published on 15 Apr 2026 - 13:19

score 148 · Answer 14 · 2026-04-15 12:10:25

148

Views

Show the following matrix has determinant = 0

Published on 15 Apr 2026 - 12:10

score 36 · Answer 15 · 2026-04-09 20:52:18

36

Views

General Results for integration of reciprocal trig functions

Published on 09 Apr 2026 - 20:52

List Question

Showing that $ \int_0^\pi \frac{\sin{(kx)}}{\sin(x)} d x = \pi $ for odd integer $k$

Why does $\sin(x) - \sin(y)=2 \cos(\frac{x+y}{2}) \sin(\frac{x-y}{2})$?

$x^2 + y^2+xy = 1$ , then find the minimum of $x^3 y + xy^3 +4$

$\sin x+\sin y+\sin z=4\cos\frac{x}{2}\cos\frac{y}{2}\cos\frac{z}{2}$

Solutions to $(x-x_0)\cos(x_0)+\sin(x_0)-\sin(x)=0$

If $a\sin^2\theta-b\cos^2\theta=a-b$, then prove $a\cos^4\theta+b\sin^4\theta=\frac{ab}{a+b}$

Calculating Arc Hyperbolic CoSecant faster than using a standard power series

Fourier Series for $\cos^3(x)$

Finding a point on a circle in 3D space which is a given distance away from another point

Sum this series: $1+\cos{\theta}\sec{\theta}+\cos{2\theta}\sec^2{\theta}+\cdots+\cos{n\theta}\sec^n{\theta}$

Sums of trigonometric functions and polynomials

integral of $\sec x \tan x$

If $(1-\cos{x})^{n+1}=\sum_{k=0}^\infty c_k\cos{kt}$ for some integers $c_k$, then what is $\sum_{k=0}^\infty kc_k$?

Show the following matrix has determinant = 0

General Results for integration of reciprocal trig functions

Trending Questions

Popular # Hahtags

Popular Questions